Subgroups — C₂×C₁₉×#2562 #18040855

Order 4864.

3006 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2562	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₉×#400	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#394	C₂	1	2	yes	maximal
6	C₂×C₁₉×#388	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₉×#380	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#380	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₁₉×#125	—	2	8	no	—
13	C₂×C₁₉×#125	C₂²	1	8	yes	complemented
14	C₂×C₄×D₄×C₁₉	—	2	8	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
25	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#400	C₂²	1	16	yes	complemented
28	C₁₉×#394	C₂²	1	16	yes	—
29	C₁₉×#388	C₂²	1	32	yes	complemented
30	C₁₉×#380	C₂²	1	16	yes	complemented
31	C₁₉×#380	C₂²	1	16	yes	complemented
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	complemented
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂×C₁₉×#95	C₂²	1	4	yes	—
35	C₂×C₁₉×#95	C₂²	1	4	yes	—
36	C₂⁵×C₁₉	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₉	—	2	8	no	—
38	C₂²×D₄×C₁₉	—	2	4	no	—
39	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
40	C₂³×C₄×C₁₉	—	2	8	no	—
41	C₂³×C₄×C₁₉	—	2	8	no	—
42	C₂³×C₄×C₁₉	—	2	8	no	—
43	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₁₉×#125	—	2	32	no	—
52	C₄×D₄×C₁₉	—	2	32	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
68	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
69	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
71	C₂×C₄²×C₁₉	—	4	4	no	—
72	C₂×C₄²×C₁₉	D₄	1	8	yes	—
73	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
75	C₁₉×#95	C₂³	1	8	yes	—
76	C₁₉×#95	C₂³	1	16	yes	—
77	C₁₉×#95	C₂³	1	16	yes	—
78	C₂⁴×C₁₉	—	2	4	no	—
79	C₂⁴×C₁₉	—	2	4	no	—
80	C₂⁴×C₁₉	—	2	4	no	—
81	C₂⁴×C₁₉	—	2	4	no	—
82	C₂⁴×C₁₉	—	2	4	no	—
83	C₂⁴×C₁₉	—	2	4	no	—
84	C₂⁴×C₁₉	#41	1	8	yes	—
85	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
86	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
87	C₂×D₄×C₁₉	—	2	32	no	—
88	C₂×D₄×C₁₉	—	2	16	no	—
89	C₂×D₄×C₁₉	—	2	8	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	8	no	—
97	C₂²×C₄×C₁₉	—	2	8	no	—
98	C₂²×C₄×C₁₉	—	2	8	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	8	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	16	no	—
105	C₂²×C₄×C₁₉	—	2	16	no	—
106	C₂²×C₄×C₁₉	—	2	16	no	—
107	C₂²×C₄×C₁₉	—	4	32	no	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₁₉	#41	1	8	yes	—
112	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
119	C₄⋊C₄×C₁₉	—	2	8	no	—
120	C₄⋊C₄×C₁₉	—	2	16	no	—
121	C₄⋊C₄×C₁₉	—	2	16	no	—
122	C₄⋊C₄×C₁₉	—	2	8	no	—
123	C₄⋊C₄×C₁₉	—	2	8	no	—
124	C₄⋊C₄×C₁₉	—	2	16	no	—
125	C₂²⋊C₄×C₁₉	—	2	32	no	—
126	C₂²⋊C₄×C₁₉	—	2	16	no	—
127	C₂²⋊C₄×C₁₉	—	4	16	no	—
128	C₄²×C₁₉	—	4	8	no	—
129	C₄²×C₁₉	C₂×D₄	1	16	yes	—
130	C₂×#2562	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₁₉	—	2	16	no	—
132	C₂³×C₁₉	—	2	16	no	—
133	C₂³×C₁₉	—	2	16	no	—
134	C₂³×C₁₉	—	2	4	no	—
135	C₂³×C₁₉	—	2	4	no	—
136	C₂³×C₁₉	—	2	4	no	—
137	C₂³×C₁₉	—	2	4	no	—
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	—	4	8	no	—
141	C₂³×C₁₉	—	4	8	no	—
142	C₂³×C₁₉	—	4	8	no	—
143	C₂³×C₁₉	—	4	8	no	—
144	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
145	C₂³×C₁₉	C₂×#41	1	8	yes	—
146	C₂³×C₁₉	C₂×#41	1	4	yes	—
147	C₂³×C₁₉	C₂×#41	1	4	yes	—
148	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
149	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
150	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
151	D₄×C₁₉	—	2	32	no	—
152	C₂×C₄×C₁₉	—	2	8	no	—
153	C₂×C₄×C₁₉	—	2	8	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	2	8	no	—
162	C₂×C₄×C₁₉	—	2	8	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	8	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	4	8	no	—
169	C₂×C₄×C₁₉	—	4	8	no	—
170	C₂×C₄×C₁₉	—	4	8	no	—
171	C₂×C₄×C₁₉	—	4	16	no	—
172	C₂×C₄×C₁₉	—	4	32	no	—
173	C₂×C₄×C₁₉	#124	1	16	yes	—
174	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
175	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
176	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
177	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
178	C₂²×#125	C₂×C₁₉	1	1	yes	characteristic, complemented
179	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic
180	#2562	C₂×C₁₉	1	16	yes	direct product factor
181	C₂×#400	C₂×C₁₉	1	2	yes	complemented
182	C₂×#394	C₂×C₁₉	1	2	yes	—
183	C₂×#388	C₂×C₁₉	1	4	yes	complemented
184	C₂×#380	C₂×C₁₉	1	2	yes	complemented
185	C₂×#380	C₂×C₁₉	1	2	yes	complemented
186	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
187	C₂²×C₁₉	—	2	8	no	—
188	C₂²×C₁₉	—	2	8	no	—
189	C₂²×C₁₉	—	2	8	no	—
190	C₂²×C₁₉	—	4	32	no	—
191	C₂²×C₁₉	—	4	4	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	4	4	no	—
195	C₂²×C₁₉	#525	1	4	yes	—
196	C₂²×C₁₉	C₂×#124	1	4	yes	—
197	C₂²×C₁₉	#537	1	4	yes	—
198	C₂²×C₁₉	#552	1	8	yes	—
199	C₂²×C₁₉	#553	1	8	yes	—
200	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
201	C₂²×C₁₉	C₂²×#41	1	2	yes	—
202	C₂²×C₁₉	C₂²×#41	1	2	yes	—
203	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
204	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
205	C₄×C₁₉	—	2	4	no	—
206	C₄×C₁₉	—	2	4	no	—
207	C₄×C₁₉	—	4	4	no	—
208	C₄×C₁₉	—	4	4	no	—
209	C₄×C₁₉	—	4	4	no	—
210	C₄×C₁₉	—	4	8	no	—
211	C₄×C₁₉	C₂×#124	1	8	yes	—
212	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
213	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
214	C₂×#125	—	2	8	no	—
215	C₂×#125	C₂²×C₁₉	1	8	yes	complemented
216	C₂×C₄×D₄	—	2	8	no	—
217	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
219	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
222	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
224	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
225	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
226	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
227	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
228	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
229	#400	C₂²×C₁₉	1	16	yes	complemented
230	#394	C₂²×C₁₉	1	16	yes	—
231	#388	C₂²×C₁₉	1	32	yes	complemented
232	#380	C₂²×C₁₉	1	16	yes	complemented
233	#380	C₂²×C₁₉	1	16	yes	complemented
234	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	complemented
235	C₂×#95	C₂²×C₁₉	1	2	yes	—
236	C₂×#95	C₂²×C₁₉	1	4	yes	—
237	C₂×#95	C₂²×C₁₉	1	4	yes	—
238	C₂×C₁₉	—	4	8	no	—
239	C₂×C₁₉	#2562	1	8	yes	direct product factor
240	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
241	C₂×C₁₉	C₂²×#124	1	1	yes	characteristic
242	C₂×C₁₉	C₂×#537	1	1	yes	characteristic
243	C₂×C₁₉	C₂×#552	1	2	yes	—
244	C₂×C₁₉	C₂×#553	1	2	yes	—
245	C₂⁵	C₂³×C₁₉	1	2	yes	—
246	C₂²×D₄	—	2	8	no	—
247	C₂²×D₄	—	2	4	no	—
248	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	—	2	8	no	—
251	C₂³×C₄	—	2	8	no	—
252	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
253	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
254	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
255	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
257	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
260	#125	—	2	32	no	—
261	C₄×D₄	—	2	32	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	8	no	—
264	C₂×C₄⋊C₄	—	2	8	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	8	no	—
268	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
274	C₂×C₂²⋊C₄	—	2	16	no	—
275	C₂×C₂²⋊C₄	—	2	8	no	—
276	C₂×C₂²⋊C₄	—	4	8	no	—
277	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
280	C₂×C₄²	—	4	4	no	—
281	C₂×C₄²	D₄×C₁₉	1	8	yes	—
282	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
283	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
284	#95	C₂³×C₁₉	1	8	yes	—
285	#95	C₂³×C₁₉	1	16	yes	—
286	#95	C₂³×C₁₉	1	16	yes	—
287	C₁₉	C₂×#2562	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁴	—	2	4	no	—
289	C₂⁴	—	2	4	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	4	no	—
294	C₂⁴	#41×C₁₉	1	8	yes	—
295	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
296	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
297	C₂×D₄	—	2	32	no	—
298	C₂×D₄	—	2	16	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	16	no	—
315	C₂²×C₄	—	2	16	no	—
316	C₂²×C₄	—	2	16	no	—
317	C₂²×C₄	—	4	32	no	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
321	C₂²×C₄	#41×C₁₉	1	8	yes	—
322	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
324	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
326	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
328	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	16	no	—
331	C₄⋊C₄	—	2	16	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	2	16	no	—
335	C₂²⋊C₄	—	2	32	no	—
336	C₂²⋊C₄	—	2	16	no	—
337	C₂²⋊C₄	—	4	16	no	—
338	C₄²	—	4	8	no	—
339	C₄²	C₂×D₄×C₁₉	1	16	yes	—
340	C₂³	—	2	16	no	—
341	C₂³	—	2	16	no	—
342	C₂³	—	2	16	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	4	8	no	—
350	C₂³	—	4	8	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	4	8	no	—
353	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
354	C₂³	C₂×#41×C₁₉	1	8	yes	—
355	C₂³	C₂×#41×C₁₉	1	4	yes	—
356	C₂³	C₂×#41×C₁₉	1	4	yes	—
357	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
358	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
359	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
360	D₄	—	2	32	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	8	no	—
380	C₂×C₄	—	4	16	no	—
381	C₂×C₄	—	4	32	no	—
382	C₂×C₄	C₁₉×#124	1	16	yes	—
383	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
384	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
385	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
386	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
387	C₂²	—	2	8	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	2	8	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	32	no	—
395	C₂²	C₁₉×#525	1	4	yes	—
396	C₂²	C₂×C₁₉×#124	1	4	yes	—
397	C₂²	C₁₉×#537	1	4	yes	—
398	C₂²	C₁₉×#552	1	8	yes	—
399	C₂²	C₁₉×#553	1	8	yes	—
400	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
401	C₂²	C₂²×#41×C₁₉	1	2	yes	—
402	C₂²	C₂²×#41×C₁₉	1	2	yes	—
403	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
404	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
405	C₄	—	2	4	no	—
406	C₄	—	2	4	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	4	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	8	no	—
411	C₄	C₂×C₁₉×#124	1	8	yes	—
412	C₂	—	4	8	no	—
413	C₂	C₁₉×#2562	1	8	yes	direct product factor
414	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
415	C₂	C₂²×C₁₉×#124	1	1	yes	characteristic
416	C₂	C₂×C₁₉×#537	1	1	yes	characteristic
417	C₂	C₂×C₁₉×#552	1	2	yes	—
418	C₂	C₂×C₁₉×#553	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#125	C₂	semidirect
3. C₁₉×#2562	C₂	direct (N × H)
4. C₂×C₁₉×#400	C₂	semidirect
6. C₂×C₁₉×#388	C₂	semidirect
7. C₂×C₁₉×#380	C₂	semidirect
8. C₂×C₁₉×#380	C₂	semidirect
9. C₂×C₄×C₄⋊C₄×C₁₉	C₂	semidirect
13. C₂×C₁₉×#125	C₂²	semidirect
27. C₁₉×#400	C₂²	semidirect
29. C₁₉×#388	C₂²	semidirect
30. C₁₉×#380	C₂²	semidirect
31. C₁₉×#380	C₂²	semidirect
32. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
130. C₂×#2562	C₁₉	direct (N × H)
178. C₂²×#125	C₂×C₁₉	semidirect
180. #2562	C₂×C₁₉	direct (N × H)
181. C₂×#400	C₂×C₁₉	semidirect
183. C₂×#388	C₂×C₁₉	semidirect
184. C₂×#380	C₂×C₁₉	semidirect
185. C₂×#380	C₂×C₁₉	semidirect
186. C₂×C₄×C₄⋊C₄	C₂×C₁₉	semidirect
215. C₂×#125	C₂²×C₁₉	semidirect
229. #400	C₂²×C₁₉	semidirect
231. #388	C₂²×C₁₉	semidirect
232. #380	C₂²×C₁₉	semidirect
233. #380	C₂²×C₁₉	semidirect
234. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
239. C₂×C₁₉	#2562	direct (N × H)
287. C₁₉	C₂×#2562	direct (N × H)
413. C₂	C₁₉×#2562	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#125	2
C₂²×C₄×D₄×C₁₉	2
C₁₉×#2562	2
C₂×C₁₉×#400	2
C₂×C₁₉×#394	2
C₂×C₁₉×#388	2
C₂×C₁₉×#380	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₂×#2562	19

Subgroups — C2×C19×#2562 #18040855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2562 #18040855