Subgroups — C₁₉×#14724 #18020683

Order 4864.

6582 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#394	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#379	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#379	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1438	C₂	1	4	yes	maximal, complemented
7	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁶×C₁₉	C₂²	1	2	yes	—
9	C₂³×D₄×C₁₉	—	2	8	no	—
10	C₂³×D₄×C₁₉	—	2	16	no	—
11	C₂³×D₄×C₁₉	—	2	4	no	—
12	C₂³×D₄×C₁₉	C₂²	1	4	yes	—
13	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	complemented
20	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
21	C₁₉×#394	—	2	16	no	—
22	C₁₉×#385	—	2	4	no	—
23	C₁₉×#379	—	2	8	no	—
24	C₁₉×#379	—	2	8	no	—
25	C₂×C₁₉×#95	C₂²	1	4	yes	complemented
26	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
27	C₂⁵×C₁₉	—	2	16	no	—
28	C₂⁵×C₁₉	—	2	4	no	—
29	C₂⁵×C₁₉	—	2	4	no	—
30	C₂⁵×C₁₉	—	2	4	no	—
31	C₂⁵×C₁₉	—	2	4	no	—
32	C₂⁵×C₁₉	—	2	4	no	—
33	C₂⁵×C₁₉	—	2	4	no	—
34	C₂⁵×C₁₉	—	4	8	no	—
35	C₂⁵×C₁₉	D₄	1	8	yes	—
36	C₂⁵×C₁₉	C₂³	1	4	yes	—
37	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₁₉	—	2	128	no	—
39	C₂²×D₄×C₁₉	—	2	32	no	—
40	C₂²×D₄×C₁₉	—	2	64	no	—
41	C₂²×D₄×C₁₉	—	2	16	no	—
42	C₂²×D₄×C₁₉	—	2	16	no	—
43	C₂²×D₄×C₁₉	—	2	8	no	—
44	C₂²×D₄×C₁₉	—	2	8	no	—
45	C₂²×D₄×C₁₉	D₄	1	16	yes	—
46	C₂³×C₄×C₁₉	—	2	4	no	—
47	C₂³×C₄×C₁₉	—	2	8	no	—
48	C₂³×C₄×C₁₉	D₄	1	4	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
70	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	complemented
71	C₁₉×#95	—	2	4	no	—
72	C₁₉×#95	—	2	8	no	—
73	C₂⁴×C₁₉	—	2	4	no	—
74	C₂⁴×C₁₉	—	2	4	no	—
75	C₂⁴×C₁₉	—	2	32	no	—
76	C₂⁴×C₁₉	—	2	32	no	—
77	C₂⁴×C₁₉	—	2	32	no	—
78	C₂⁴×C₁₉	—	2	16	no	—
79	C₂⁴×C₁₉	—	2	4	no	—
80	C₂⁴×C₁₉	—	2	4	no	—
81	C₂⁴×C₁₉	—	2	4	no	—
82	C₂⁴×C₁₉	—	2	8	no	—
83	C₂⁴×C₁₉	—	2	4	no	—
84	C₂⁴×C₁₉	—	2	4	no	—
85	C₂⁴×C₁₉	—	2	4	no	—
86	C₂⁴×C₁₉	—	2	8	no	—
87	C₂⁴×C₁₉	—	2	8	no	—
88	C₂⁴×C₁₉	—	2	16	no	—
89	C₂⁴×C₁₉	—	2	16	no	—
90	C₂⁴×C₁₉	—	4	16	no	—
91	C₂⁴×C₁₉	—	4	32	no	—
92	C₂⁴×C₁₉	—	4	32	no	—
93	C₂⁴×C₁₉	—	4	32	no	—
94	C₂⁴×C₁₉	—	4	32	no	—
95	C₂⁴×C₁₉	—	4	16	no	—
96	C₂⁴×C₁₉	—	4	16	no	—
97	C₂⁴×C₁₉	—	4	8	no	—
98	C₂⁴×C₁₉	—	4	8	no	—
99	C₂⁴×C₁₉	—	4	8	no	—
100	C₂⁴×C₁₉	—	4	8	no	—
101	C₂⁴×C₁₉	C₂×D₄	1	8	yes	—
102	C₂⁴×C₁₉	C₂×D₄	1	16	yes	—
103	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
104	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
105	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
106	C₂⁴×C₁₉	#41	1	2	yes	—
107	C₂⁴×C₁₉	#41	1	4	yes	—
108	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
109	C₂×D₄×C₁₉	—	2	256	no	—
110	C₂×D₄×C₁₉	—	2	32	no	—
111	C₂×D₄×C₁₉	—	2	64	no	—
112	C₂×D₄×C₁₉	—	2	32	no	—
113	C₂×D₄×C₁₉	—	2	64	no	—
114	C₂×D₄×C₁₉	—	2	32	no	—
115	C₂²×C₄×C₁₉	—	2	32	no	—
116	C₂²×C₄×C₁₉	—	2	8	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	16	no	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	4	no	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	2	8	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	4	no	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	8	no	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	complemented
138	C₄⋊C₄×C₁₉	—	4	8	no	—
139	C₂²⋊C₄×C₁₉	—	2	8	no	—
140	C₂²⋊C₄×C₁₉	—	4	32	no	—
141	C₂²⋊C₄×C₁₉	—	4	16	no	—
142	C₂²⋊C₄×C₁₉	—	4	16	no	—
143	C₂²⋊C₄×C₁₉	—	4	4	no	—
144	C₂²⋊C₄×C₁₉	—	4	8	no	—
145	#14724	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂³×C₁₉	—	2	8	no	—
147	C₂³×C₁₉	—	2	4	no	—
148	C₂³×C₁₉	—	2	8	no	—
149	C₂³×C₁₉	—	2	4	no	—
150	C₂³×C₁₉	—	2	8	no	—
151	C₂³×C₁₉	—	2	8	no	—
152	C₂³×C₁₉	—	2	16	no	—
153	C₂³×C₁₉	—	2	64	no	—
154	C₂³×C₁₉	—	2	8	no	—
155	C₂³×C₁₉	—	2	8	no	—
156	C₂³×C₁₉	—	2	16	no	—
157	C₂³×C₁₉	—	2	16	no	—
158	C₂³×C₁₉	—	2	8	no	—
159	C₂³×C₁₉	—	2	8	no	—
160	C₂³×C₁₉	—	2	8	no	—
161	C₂³×C₁₉	—	2	8	no	—
162	C₂³×C₁₉	—	2	16	no	—
163	C₂³×C₁₉	—	2	16	no	—
164	C₂³×C₁₉	—	2	16	no	—
165	C₂³×C₁₉	—	2	16	no	—
166	C₂³×C₁₉	—	4	64	no	—
167	C₂³×C₁₉	—	4	64	no	—
168	C₂³×C₁₉	—	4	32	no	—
169	C₂³×C₁₉	—	4	64	no	—
170	C₂³×C₁₉	—	4	64	no	—
171	C₂³×C₁₉	—	4	64	no	—
172	C₂³×C₁₉	—	4	64	no	—
173	C₂³×C₁₉	—	4	4	no	—
174	C₂³×C₁₉	—	4	4	no	—
175	C₂³×C₁₉	—	4	4	no	—
176	C₂³×C₁₉	—	4	4	no	—
177	C₂³×C₁₉	—	4	8	no	—
178	C₂³×C₁₉	—	4	8	no	—
179	C₂³×C₁₉	—	4	8	no	—
180	C₂³×C₁₉	—	4	8	no	—
181	C₂³×C₁₉	—	4	8	no	—
182	C₂³×C₁₉	—	4	8	no	—
183	C₂³×C₁₉	—	4	32	no	—
184	C₂³×C₁₉	#120	1	16	yes	—
185	C₂³×C₁₉	#120	1	4	yes	—
186	C₂³×C₁₉	#121	1	4	yes	—
187	C₂³×C₁₉	#121	1	8	yes	—
188	C₂³×C₁₉	#123	1	8	yes	—
189	C₂³×C₁₉	#124	1	4	yes	—
190	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
191	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
193	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
194	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
195	C₂³×C₁₉	C₂×#41	1	2	yes	—
196	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
197	D₄×C₁₉	—	2	128	no	—
198	C₂×C₄×C₁₉	—	2	32	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	16	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	8	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	4	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	4	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	4	no	—
213	C₂×C₄×C₁₉	—	4	4	no	—
214	C₂×C₄×C₁₉	—	4	4	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	8	no	—
217	C₂×C₄×C₁₉	—	4	8	no	—
218	C₂×C₄×C₁₉	#120	1	8	yes	—
219	C₂⁴×D₄	C₂×C₁₉	1	1	yes	characteristic
220	C₂×#394	C₂×C₁₉	1	4	yes	complemented
221	C₂×#385	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₂×#379	C₂×C₁₉	1	2	yes	complemented
223	C₂×#379	C₂×C₁₉	1	2	yes	complemented
224	#1438	C₂×C₁₉	1	4	yes	complemented
225	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic, complemented
226	C₂²×C₁₉	—	2	4	no	—
227	C₂²×C₁₉	—	2	4	no	—
228	C₂²×C₁₉	—	2	16	no	—
229	C₂²×C₁₉	—	2	8	no	—
230	C₂²×C₁₉	—	2	16	no	—
231	C₂²×C₁₉	—	2	8	no	—
232	C₂²×C₁₉	—	2	16	no	—
233	C₂²×C₁₉	—	2	16	no	—
234	C₂²×C₁₉	—	2	16	no	—
235	C₂²×C₁₉	—	4	128	no	—
236	C₂²×C₁₉	—	4	8	no	—
237	C₂²×C₁₉	—	4	8	no	—
238	C₂²×C₁₉	—	4	8	no	—
239	C₂²×C₁₉	—	4	16	no	—
240	C₂²×C₁₉	—	4	16	no	—
241	C₂²×C₁₉	—	4	8	no	—
242	C₂²×C₁₉	—	4	16	no	—
243	C₂²×C₁₉	—	4	16	no	—
244	C₂²×C₁₉	#394	1	8	yes	complemented
245	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
246	C₂²×C₁₉	C₂×#120	1	4	yes	—
247	C₂²×C₁₉	C₂×#120	1	2	yes	—
248	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
249	C₂²×C₁₉	C₂×#121	1	2	yes	—
250	C₂²×C₁₉	C₂×#123	1	2	yes	—
251	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
252	C₂²×C₁₉	#534	1	4	yes	—
253	C₂²×C₁₉	#535	1	2	yes	—
254	C₂²×C₁₉	D₄²	1	4	yes	—
255	C₂²×C₁₉	#546	1	4	yes	—
256	C₂²×C₁₉	#546	1	8	yes	—
257	C₄×C₁₉	—	2	8	no	—
258	C₄×C₁₉	—	4	4	no	—
259	C₄×C₁₉	—	8	1	no	—
260	C₄×C₁₉	—	8	1	no	—
261	C₄×C₁₉	—	8	4	no	—
262	C₂⁶	C₂²×C₁₉	1	2	yes	—
263	C₂³×D₄	—	2	8	no	—
264	C₂³×D₄	—	2	16	no	—
265	C₂³×D₄	—	2	4	no	—
266	C₂³×D₄	C₂²×C₁₉	1	4	yes	—
267	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
269	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
270	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
272	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
273	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	complemented
274	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
275	#394	—	2	16	no	—
276	#385	—	2	4	no	—
277	#379	—	2	8	no	—
278	#379	—	2	8	no	—
279	C₂×#95	C₂²×C₁₉	1	4	yes	complemented
280	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
281	C₂×C₁₉	—	2	8	no	—
282	C₂×C₁₉	—	4	16	no	—
283	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
284	C₂×C₁₉	#2405	1	4	yes	—
285	C₂×C₁₉	#2408	1	2	yes	—
286	C₂×C₁₉	#2410	1	4	yes	—
287	C₂×C₁₉	#2435	1	2	yes	—
288	C₂×C₁₉	#2613	1	1	yes	characteristic
289	C₂×C₁₉	#2846	1	1	yes	characteristic
290	C₂⁵	—	2	16	no	—
291	C₂⁵	—	2	4	no	—
292	C₂⁵	—	2	4	no	—
293	C₂⁵	—	2	4	no	—
294	C₂⁵	—	2	4	no	—
295	C₂⁵	—	2	4	no	—
296	C₂⁵	—	2	4	no	—
297	C₂⁵	—	4	8	no	—
298	C₂⁵	D₄×C₁₉	1	8	yes	—
299	C₂⁵	C₂³×C₁₉	1	4	yes	—
300	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
301	C₂²×D₄	—	2	128	no	—
302	C₂²×D₄	—	2	32	no	—
303	C₂²×D₄	—	2	64	no	—
304	C₂²×D₄	—	2	16	no	—
305	C₂²×D₄	—	2	16	no	—
306	C₂²×D₄	—	2	8	no	—
307	C₂²×D₄	—	2	8	no	—
308	C₂²×D₄	D₄×C₁₉	1	16	yes	—
309	C₂³×C₄	—	2	4	no	—
310	C₂³×C₄	—	2	8	no	—
311	C₂³×C₄	D₄×C₁₉	1	4	yes	—
312	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
315	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
316	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	—	2	4	no	—
318	C₂×C₄⋊C₄	—	2	8	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	4	no	—
322	C₂×C₂²⋊C₄	—	2	4	no	—
323	C₂×C₂²⋊C₄	—	2	4	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	8	no	—
326	C₂×C₂²⋊C₄	—	2	8	no	—
327	C₂×C₂²⋊C₄	—	2	16	no	—
328	C₂×C₂²⋊C₄	—	2	16	no	—
329	C₂×C₂²⋊C₄	—	2	4	no	—
330	C₂×C₂²⋊C₄	—	2	16	no	—
331	C₂×C₂²⋊C₄	—	4	8	no	—
332	C₂×C₂²⋊C₄	—	4	8	no	—
333	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	complemented
334	#95	—	2	4	no	—
335	#95	—	2	8	no	—
336	C₁₉	#14724	1	1	yes	characteristic, direct product factor, Sylow
337	C₂⁴	—	2	4	no	—
338	C₂⁴	—	2	4	no	—
339	C₂⁴	—	2	32	no	—
340	C₂⁴	—	2	32	no	—
341	C₂⁴	—	2	32	no	—
342	C₂⁴	—	2	16	no	—
343	C₂⁴	—	2	4	no	—
344	C₂⁴	—	2	4	no	—
345	C₂⁴	—	2	4	no	—
346	C₂⁴	—	2	8	no	—
347	C₂⁴	—	2	4	no	—
348	C₂⁴	—	2	4	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	2	8	no	—
351	C₂⁴	—	2	8	no	—
352	C₂⁴	—	2	16	no	—
353	C₂⁴	—	2	16	no	—
354	C₂⁴	—	4	16	no	—
355	C₂⁴	—	4	32	no	—
356	C₂⁴	—	4	32	no	—
357	C₂⁴	—	4	32	no	—
358	C₂⁴	—	4	32	no	—
359	C₂⁴	—	4	16	no	—
360	C₂⁴	—	4	16	no	—
361	C₂⁴	—	4	8	no	—
362	C₂⁴	—	4	8	no	—
363	C₂⁴	—	4	8	no	—
364	C₂⁴	—	4	8	no	—
365	C₂⁴	C₂×D₄×C₁₉	1	8	yes	—
366	C₂⁴	C₂×D₄×C₁₉	1	16	yes	—
367	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
368	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
369	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
370	C₂⁴	#41×C₁₉	1	2	yes	—
371	C₂⁴	#41×C₁₉	1	4	yes	—
372	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
373	C₂×D₄	—	2	256	no	—
374	C₂×D₄	—	2	64	no	—
375	C₂×D₄	—	2	32	no	—
376	C₂×D₄	—	2	32	no	—
377	C₂×D₄	—	2	64	no	—
378	C₂×D₄	—	2	32	no	—
379	C₂²×C₄	—	2	32	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	16	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	8	no	—
399	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
400	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
401	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	complemented
402	C₄⋊C₄	—	4	8	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	4	32	no	—
405	C₂²⋊C₄	—	4	16	no	—
406	C₂²⋊C₄	—	4	16	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	8	no	—
409	C₂³	—	2	8	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	8	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	8	no	—
414	C₂³	—	2	8	no	—
415	C₂³	—	2	16	no	—
416	C₂³	—	2	64	no	—
417	C₂³	—	2	8	no	—
418	C₂³	—	2	16	no	—
419	C₂³	—	2	16	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	2	8	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	8	no	—
425	C₂³	—	2	16	no	—
426	C₂³	—	2	16	no	—
427	C₂³	—	2	16	no	—
428	C₂³	—	2	16	no	—
429	C₂³	—	4	64	no	—
430	C₂³	—	4	64	no	—
431	C₂³	—	4	64	no	—
432	C₂³	—	4	64	no	—
433	C₂³	—	4	64	no	—
434	C₂³	—	4	64	no	—
435	C₂³	—	4	32	no	—
436	C₂³	—	4	32	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	4	4	no	—
439	C₂³	—	4	4	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	8	no	—
442	C₂³	—	4	8	no	—
443	C₂³	—	4	8	no	—
444	C₂³	—	4	8	no	—
445	C₂³	—	4	8	no	—
446	C₂³	—	4	8	no	—
447	C₂³	C₁₉×#120	1	16	yes	—
448	C₂³	C₁₉×#120	1	4	yes	—
449	C₂³	C₁₉×#121	1	4	yes	—
450	C₂³	C₁₉×#121	1	8	yes	—
451	C₂³	C₁₉×#123	1	8	yes	—
452	C₂³	C₁₉×#124	1	4	yes	—
453	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
454	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
455	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
456	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
457	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
458	C₂³	C₂×#41×C₁₉	1	2	yes	—
459	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
460	D₄	—	2	128	no	—
461	C₂×C₄	—	2	32	no	—
462	C₂×C₄	—	2	16	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	8	no	—
480	C₂×C₄	—	4	8	no	—
481	C₂×C₄	C₁₉×#120	1	8	yes	—
482	C₂²	—	2	16	no	—
483	C₂²	—	2	8	no	—
484	C₂²	—	2	16	no	—
485	C₂²	—	2	8	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	2	16	no	—
489	C₂²	—	2	16	no	—
490	C₂²	—	2	16	no	—
491	C₂²	—	4	128	no	—
492	C₂²	—	4	8	no	—
493	C₂²	—	4	16	no	—
494	C₂²	—	4	16	no	—
495	C₂²	—	4	8	no	—
496	C₂²	—	4	16	no	—
497	C₂²	—	4	16	no	—
498	C₂²	—	4	8	no	—
499	C₂²	—	4	8	no	—
500	C₂²	C₁₉×#394	1	8	yes	complemented
501	C₂²	C₂×C₁₉×#120	1	4	yes	—
502	C₂²	C₂×C₁₉×#120	1	2	yes	—
503	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
504	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
505	C₂²	C₂×C₁₉×#121	1	2	yes	—
506	C₂²	C₂×C₁₉×#123	1	2	yes	—
507	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
508	C₂²	C₁₉×#534	1	4	yes	—
509	C₂²	C₁₉×#535	1	2	yes	—
510	C₂²	D₄²×C₁₉	1	4	yes	—
511	C₂²	C₁₉×#546	1	4	yes	—
512	C₂²	C₁₉×#546	1	8	yes	—
513	C₄	—	2	8	no	—
514	C₄	—	4	4	no	—
515	C₄	—	8	4	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	1	no	—
518	C₂	—	2	8	no	—
519	C₂	—	4	16	no	—
520	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
521	C₂	C₁₉×#2405	1	4	yes	—
522	C₂	C₁₉×#2408	1	2	yes	—
523	C₂	C₁₉×#2410	1	4	yes	—
524	C₂	C₁₉×#2435	1	2	yes	—
525	C₂	C₁₉×#2613	1	1	yes	characteristic
526	C₂	C₁₉×#2846	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁴×D₄×C₁₉	C₂
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×#394	C₂	semidirect
3. C₂×C₁₉×#385	C₂	semidirect
4. C₂×C₁₉×#379	C₂	semidirect
5. C₂×C₁₉×#379	C₂	semidirect
6. C₁₉×#1438	C₂	semidirect
7. C₁₉×C₂²⋊#95	C₂	semidirect
14. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
18. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
19. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
20. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
25. C₂×C₁₉×#95	C₂²	semidirect
26. C₂×C₁₉×#95	C₂²	semidirect
70. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
137. C₂²×C₄×C₁₉	C₂×D₄	semidirect
145. #14724	C₁₉	direct (N × H)
220. C₂×#394	C₂×C₁₉	semidirect
221. C₂×#385	C₂×C₁₉	semidirect
222. C₂×#379	C₂×C₁₉	semidirect
223. C₂×#379	C₂×C₁₉	semidirect
224. #1438	C₂×C₁₉	semidirect
225. C₂²⋊#95	C₂×C₁₉	semidirect
244. C₂²×C₁₉	#394	semidirect
268. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
272. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
273. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
274. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
279. C₂×#95	C₂²×C₁₉	semidirect
280. C₂×#95	C₂²×C₁₉	semidirect
333. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
336. C₁₉	#14724	direct (N × H)
401. C₂²×C₄	C₂×D₄×C₁₉	semidirect
500. C₂²	C₁₉×#394	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₁₉	2
C₂×C₁₉×#394	2
C₂×C₁₉×#385	2
C₂×C₁₉×#379	2
C₁₉×#1438	2
C₁₉×C₂²⋊#95	2
#14724	19

Subgroups — C19×#14724 #18020683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14724 #18020683