Subgroups — C₂×C₁₉×#2021 #18029400

Order 4864.

3986 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#534	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#120	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×#99	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#379	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2021	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁶×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₁₉	—	2	2	no	—
9	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
10	C₁₉×#534	—	2	4	no	—
11	C₁₉×#534	—	2	2	no	—
12	C₁₉×#534	C₂²	1	4	yes	complemented
13	C₂×C₁₉×#123	—	2	2	no	—
14	C₂×C₁₉×#121	—	2	2	no	—
15	C₂×C₁₉×#120	—	2	8	no	—
16	C₂×C₁₉×#120	—	2	2	no	—
17	C₂×C₁₉×#120	—	2	4	no	—
18	C₂×C₁₉×#120	—	2	8	no	—
19	C₂×C₁₉×#120	C₂²	1	8	yes	complemented
20	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
21	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₂×C₁₉×#99	—	2	8	no	—
26	C₂×C₁₉×#99	C₂²	1	8	yes	complemented
27	C₁₉×#379	—	2	2	no	—
28	C₁₉×#379	C₂²	1	4	yes	complemented
29	C₁₉×#342	C₂²	1	4	yes	complemented
30	C₂⁵×C₁₉	—	2	1	no	—
31	C₂⁵×C₁₉	—	2	2	no	—
32	C₂⁵×C₁₉	—	2	1	no	—
33	C₂⁵×C₁₉	—	2	4	no	—
34	C₂⁵×C₁₉	—	2	2	no	—
35	C₂⁵×C₁₉	—	2	2	no	—
36	C₂⁵×C₁₉	—	4	8	no	—
37	C₂⁵×C₁₉	D₄	1	4	yes	complemented
38	C₂⁵×C₁₉	D₄	1	2	yes	complemented
39	C₂⁵×C₁₉	C₂³	1	2	yes	—
40	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₁₉	—	2	16	no	—
42	C₂²×D₄×C₁₉	—	2	4	no	—
43	C₂²×D₄×C₁₉	—	2	4	no	—
44	C₂²×D₄×C₁₉	—	2	4	no	—
45	C₂²×D₄×C₁₉	—	2	2	no	—
46	C₂²×D₄×C₁₉	—	2	2	no	—
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	—	2	8	no	—
50	C₂²×D₄×C₁₉	—	2	4	no	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	4	16	no	—
53	C₂²×D₄×C₁₉	D₄	1	4	yes	complemented
54	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₉	—	2	2	no	—
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	D₄	1	2	yes	complemented
58	C₂³×C₄×C₁₉	D₄	1	2	yes	complemented
59	C₁₉×#123	—	2	8	no	—
60	C₁₉×#123	—	2	8	no	—
61	C₁₉×#121	—	2	8	no	—
62	C₁₉×#121	—	2	8	no	—
63	C₁₉×#120	—	2	32	no	—
64	C₁₉×#120	—	2	8	no	—
65	C₁₉×#120	—	2	16	no	—
66	C₁₉×#120	—	2	8	no	—
67	C₁₉×#120	—	2	16	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
80	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	complemented
81	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	complemented
82	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
85	C₁₉×#99	—	2	16	no	—
86	C₂⁴×C₁₉	—	2	8	no	—
87	C₂⁴×C₁₉	—	2	16	no	—
88	C₂⁴×C₁₉	—	2	8	no	—
89	C₂⁴×C₁₉	—	2	4	no	—
90	C₂⁴×C₁₉	—	2	2	no	—
91	C₂⁴×C₁₉	—	2	4	no	—
92	C₂⁴×C₁₉	—	2	8	no	—
93	C₂⁴×C₁₉	—	2	4	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	4	no	—
96	C₂⁴×C₁₉	—	2	4	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	4	no	—
100	C₂⁴×C₁₉	—	4	16	no	—
101	C₂⁴×C₁₉	—	4	8	no	—
102	C₂⁴×C₁₉	—	4	4	no	—
103	C₂⁴×C₁₉	—	4	4	no	—
104	C₂⁴×C₁₉	—	4	8	no	—
105	C₂⁴×C₁₉	—	4	8	no	—
106	C₂⁴×C₁₉	—	4	16	no	—
107	C₂⁴×C₁₉	—	4	32	no	—
108	C₂⁴×C₁₉	—	4	16	no	—
109	C₂⁴×C₁₉	—	4	8	no	—
110	C₂⁴×C₁₉	—	4	2	no	—
111	C₂⁴×C₁₉	—	4	1	no	—
112	C₂⁴×C₁₉	—	4	1	no	—
113	C₂⁴×C₁₉	—	4	4	no	—
114	C₂⁴×C₁₉	—	4	4	no	—
115	C₂⁴×C₁₉	—	4	2	no	—
116	C₂⁴×C₁₉	—	4	2	no	—
117	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
118	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
120	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
121	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
123	C₂⁴×C₁₉	C₂×D₄	1	4	yes	complemented
124	C₂⁴×C₁₉	C₂×D₄	1	4	yes	complemented
125	C₂⁴×C₁₉	#41	1	2	yes	—
126	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₂×D₄×C₁₉	—	2	32	no	—
128	C₂×D₄×C₁₉	—	2	8	no	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	8	no	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	2	4	no	—
135	C₂×D₄×C₁₉	—	2	4	no	—
136	C₂×D₄×C₁₉	—	2	4	no	—
137	C₂×D₄×C₁₉	—	2	4	no	—
138	C₂×D₄×C₁₉	—	2	8	no	—
139	C₂×D₄×C₁₉	—	4	32	no	—
140	C₂×D₄×C₁₉	—	4	64	no	—
141	C₂×D₄×C₁₉	—	4	4	no	—
142	C₂×D₄×C₁₉	—	4	4	no	—
143	C₂×D₄×C₁₉	—	4	4	no	—
144	C₂×D₄×C₁₉	—	4	4	no	—
145	C₂×D₄×C₁₉	—	4	4	no	—
146	C₂×D₄×C₁₉	—	4	4	no	—
147	C₂×D₄×C₁₉	—	4	4	no	—
148	C₂×D₄×C₁₉	—	4	4	no	—
149	C₂×D₄×C₁₉	—	8	4	no	—
150	C₂²×C₄×C₁₉	—	2	4	no	—
151	C₂²×C₄×C₁₉	—	2	8	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	4	no	—
156	C₂²×C₄×C₁₉	—	2	4	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	4	8	no	—
160	C₂²×C₄×C₁₉	—	4	4	no	—
161	C₂²×C₄×C₁₉	—	4	4	no	—
162	C₂²×C₄×C₁₉	—	4	2	no	—
163	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	complemented
164	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	complemented
165	C₄⋊C₄×C₁₉	—	2	8	no	—
166	C₂²⋊C₄×C₁₉	—	2	32	no	—
167	C₂²⋊C₄×C₁₉	—	2	16	no	—
168	C₂²⋊C₄×C₁₉	—	2	8	no	—
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	4	16	no	—
174	C₂²⋊C₄×C₁₉	—	4	2	no	—
175	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	complemented
176	C₂×#2021	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₁₉	—	2	4	no	—
178	C₂³×C₁₉	—	2	8	no	—
179	C₂³×C₁₉	—	2	8	no	—
180	C₂³×C₁₉	—	2	16	no	—
181	C₂³×C₁₉	—	2	32	no	—
182	C₂³×C₁₉	—	2	16	no	—
183	C₂³×C₁₉	—	2	8	no	—
184	C₂³×C₁₉	—	2	4	no	—
185	C₂³×C₁₉	—	2	4	no	—
186	C₂³×C₁₉	—	2	4	no	—
187	C₂³×C₁₉	—	2	4	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	4	no	—
190	C₂³×C₁₉	—	4	4	no	—
191	C₂³×C₁₉	—	4	8	no	—
192	C₂³×C₁₉	—	4	8	no	—
193	C₂³×C₁₉	—	4	4	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	4	no	—
196	C₂³×C₁₉	—	4	8	no	—
197	C₂³×C₁₉	—	4	8	no	—
198	C₂³×C₁₉	—	4	16	no	—
199	C₂³×C₁₉	—	4	16	no	—
200	C₂³×C₁₉	—	4	16	no	—
201	C₂³×C₁₉	—	4	8	no	—
202	C₂³×C₁₉	—	4	32	no	—
203	C₂³×C₁₉	—	4	32	no	—
204	C₂³×C₁₉	—	4	16	no	—
205	C₂³×C₁₉	—	4	16	no	—
206	C₂³×C₁₉	—	4	8	no	—
207	C₂³×C₁₉	—	4	8	no	—
208	C₂³×C₁₉	—	4	16	no	—
209	C₂³×C₁₉	—	4	32	no	—
210	C₂³×C₁₉	—	4	16	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	—	4	4	no	—
213	C₂³×C₁₉	—	4	2	no	—
214	C₂³×C₁₉	—	4	8	no	—
215	C₂³×C₁₉	—	4	4	no	—
216	C₂³×C₁₉	—	4	4	no	—
217	C₂³×C₁₉	—	4	8	no	—
218	C₂³×C₁₉	—	4	4	no	—
219	C₂³×C₁₉	—	4	4	no	—
220	C₂³×C₁₉	—	4	8	no	—
221	C₂³×C₁₉	—	8	4	no	—
222	C₂³×C₁₉	—	8	8	no	—
223	C₂³×C₁₉	#120	1	2	yes	—
224	C₂³×C₁₉	#120	1	4	yes	—
225	C₂³×C₁₉	#120	1	1	yes	characteristic
226	C₂³×C₁₉	#120	1	4	yes	—
227	C₂³×C₁₉	#120	1	1	yes	characteristic
228	C₂³×C₁₉	#121	1	4	yes	—
229	C₂³×C₁₉	#121	1	2	yes	—
230	C₂³×C₁₉	#121	1	4	yes	—
231	C₂³×C₁₉	#121	1	2	yes	—
232	C₂³×C₁₉	#127	1	2	yes	—
233	C₂³×C₁₉	#127	1	2	yes	—
234	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
235	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
238	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
239	D₄×C₁₉	—	4	64	no	—
240	D₄×C₁₉	—	4	4	no	—
241	D₄×C₁₉	—	4	4	no	—
242	D₄×C₁₉	—	4	4	no	—
243	D₄×C₁₉	—	4	4	no	—
244	D₄×C₁₉	—	4	8	no	—
245	D₄×C₁₉	—	4	8	no	—
246	D₄×C₁₉	—	8	8	no	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	4	no	—
249	C₂×C₄×C₁₉	—	2	8	no	—
250	C₂×C₄×C₁₉	—	2	4	no	—
251	C₂×C₄×C₁₉	—	2	4	no	—
252	C₂×C₄×C₁₉	—	4	8	no	—
253	C₂×C₄×C₁₉	—	4	16	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	—	4	4	no	—
258	C₂×C₄×C₁₉	—	4	4	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	8	2	no	—
261	C₂×C₄×C₁₉	—	8	4	no	—
262	C₂×#534	C₂×C₁₉	1	1	yes	characteristic, complemented
263	C₂²×#120	C₂×C₁₉	1	2	yes	complemented
264	C₂²×#99	C₂×C₁₉	1	2	yes	complemented
265	C₂×#379	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#2021	C₂×C₁₉	1	8	yes	direct product factor
267	C₂×#342	C₂×C₁₉	1	1	yes	characteristic, complemented
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	2	4	no	—
270	C₂²×C₁₉	—	2	2	no	—
271	C₂²×C₁₉	—	2	4	no	—
272	C₂²×C₁₉	—	2	8	no	—
273	C₂²×C₁₉	—	2	4	no	—
274	C₂²×C₁₉	—	2	4	no	—
275	C₂²×C₁₉	—	2	8	no	—
276	C₂²×C₁₉	—	2	16	no	—
277	C₂²×C₁₉	—	2	8	no	—
278	C₂²×C₁₉	—	4	4	no	—
279	C₂²×C₁₉	—	4	2	no	—
280	C₂²×C₁₉	—	4	4	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	—	4	8	no	—
286	C₂²×C₁₉	—	4	8	no	—
287	C₂²×C₁₉	—	4	4	no	—
288	C₂²×C₁₉	—	4	16	no	—
289	C₂²×C₁₉	—	4	32	no	—
290	C₂²×C₁₉	—	4	16	no	—
291	C₂²×C₁₉	—	4	8	no	—
292	C₂²×C₁₉	—	4	4	no	—
293	C₂²×C₁₉	—	4	8	no	—
294	C₂²×C₁₉	—	4	16	no	—
295	C₂²×C₁₉	—	4	4	no	—
296	C₂²×C₁₉	—	4	8	no	—
297	C₂²×C₁₉	—	8	4	no	—
298	C₂²×C₁₉	—	8	8	no	—
299	C₂²×C₁₉	—	8	8	no	—
300	C₂²×C₁₉	#392	1	4	yes	—
301	C₂²×C₁₉	#392	1	2	yes	—
302	C₂²×C₁₉	#392	1	2	yes	—
303	C₂²×C₁₉	B(4,𝔽₂)	1	4	yes	—
304	C₂²×C₁₉	C₂×#120	1	2	yes	—
305	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
306	C₂²×C₁₉	C₂×#121	1	2	yes	—
307	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
308	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
309	C₄×C₁₉	—	4	8	no	—
310	C₄×C₁₉	—	4	4	no	—
311	C₄×C₁₉	—	4	4	no	—
312	C₄×C₁₉	—	8	2	no	—
313	C₂⁶	C₂²×C₁₉	1	1	yes	characteristic
314	C₂³×D₄	—	2	2	no	—
315	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
316	#534	—	2	4	no	—
317	#534	—	2	2	no	—
318	#534	C₂²×C₁₉	1	4	yes	complemented
319	C₂×#123	—	2	2	no	—
320	C₂×#121	—	2	2	no	—
321	C₂×#120	—	2	8	no	—
322	C₂×#120	—	2	2	no	—
323	C₂×#120	—	2	4	no	—
324	C₂×#120	—	2	8	no	—
325	C₂×#120	C₂²×C₁₉	1	8	yes	complemented
326	C₂²×C₂²⋊C₄	—	2	2	no	—
327	C₂²×C₂²⋊C₄	—	2	2	no	—
328	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
331	C₂×#99	—	2	8	no	—
332	C₂×#99	C₂²×C₁₉	1	8	yes	complemented
333	#379	—	2	2	no	—
334	#379	C₂²×C₁₉	1	4	yes	complemented
335	#342	C₂²×C₁₉	1	4	yes	complemented
336	C₂×C₁₉	—	2	2	no	—
337	C₂×C₁₉	—	2	1	no	—
338	C₂×C₁₉	—	2	1	no	—
339	C₂×C₁₉	—	2	2	no	—
340	C₂×C₁₉	—	2	4	no	—
341	C₂×C₁₉	—	2	2	no	—
342	C₂×C₁₉	—	4	8	no	—
343	C₂×C₁₉	—	8	4	no	—
344	C₂×C₁₉	#2021	1	4	yes	direct product factor
345	C₂×C₁₉	C₂×#392	1	1	yes	characteristic
346	C₂×C₁₉	C₂×B(4,𝔽₂)	1	2	yes	—
347	C₂⁵	—	2	1	no	—
348	C₂⁵	—	2	2	no	—
349	C₂⁵	—	2	4	no	—
350	C₂⁵	—	2	2	no	—
351	C₂⁵	—	2	1	no	—
352	C₂⁵	—	2	2	no	—
353	C₂⁵	—	4	8	no	—
354	C₂⁵	D₄×C₁₉	1	4	yes	complemented
355	C₂⁵	D₄×C₁₉	1	2	yes	complemented
356	C₂⁵	C₂³×C₁₉	1	2	yes	—
357	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
358	C₂²×D₄	—	2	16	no	—
359	C₂²×D₄	—	2	4	no	—
360	C₂²×D₄	—	2	4	no	—
361	C₂²×D₄	—	2	2	no	—
362	C₂²×D₄	—	2	2	no	—
363	C₂²×D₄	—	2	2	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	4	no	—
366	C₂²×D₄	—	2	8	no	—
367	C₂²×D₄	—	2	4	no	—
368	C₂²×D₄	—	2	2	no	—
369	C₂²×D₄	—	4	16	no	—
370	C₂²×D₄	D₄×C₁₉	1	4	yes	complemented
371	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
372	C₂³×C₄	—	2	2	no	—
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	D₄×C₁₉	1	2	yes	complemented
375	C₂³×C₄	D₄×C₁₉	1	2	yes	complemented
376	#123	—	2	8	no	—
377	#123	—	2	8	no	—
378	#121	—	2	8	no	—
379	#121	—	2	8	no	—
380	#120	—	2	32	no	—
381	#120	—	2	8	no	—
382	#120	—	2	16	no	—
383	#120	—	2	8	no	—
384	#120	—	2	16	no	—
385	C₂×C₄⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	16	no	—
387	C₂×C₂²⋊C₄	—	2	4	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	4	no	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	8	no	—
393	C₂×C₂²⋊C₄	—	2	4	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	8	no	—
396	C₂×C₂²⋊C₄	—	4	8	no	—
397	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	complemented
398	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	complemented
399	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
402	#99	—	2	16	no	—
403	C₁₉	C₂×#2021	1	1	yes	characteristic, direct product factor, Sylow
404	C₂⁴	—	2	8	no	—
405	C₂⁴	—	2	16	no	—
406	C₂⁴	—	2	8	no	—
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	2	8	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	—	2	4	no	—
414	C₂⁴	—	2	4	no	—
415	C₂⁴	—	2	2	no	—
416	C₂⁴	—	2	2	no	—
417	C₂⁴	—	2	4	no	—
418	C₂⁴	—	4	16	no	—
419	C₂⁴	—	4	4	no	—
420	C₂⁴	—	4	8	no	—
421	C₂⁴	—	4	4	no	—
422	C₂⁴	—	4	8	no	—
423	C₂⁴	—	4	8	no	—
424	C₂⁴	—	4	16	no	—
425	C₂⁴	—	4	32	no	—
426	C₂⁴	—	4	16	no	—
427	C₂⁴	—	4	8	no	—
428	C₂⁴	—	4	2	no	—
429	C₂⁴	—	4	1	no	—
430	C₂⁴	—	4	1	no	—
431	C₂⁴	—	4	4	no	—
432	C₂⁴	—	4	4	no	—
433	C₂⁴	—	4	2	no	—
434	C₂⁴	—	4	2	no	—
435	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
436	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
438	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
439	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
441	C₂⁴	C₂×D₄×C₁₉	1	4	yes	complemented
442	C₂⁴	C₂×D₄×C₁₉	1	4	yes	complemented
443	C₂⁴	#41×C₁₉	1	2	yes	—
444	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
445	C₂×D₄	—	2	32	no	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	8	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	8	no	—
457	C₂×D₄	—	4	32	no	—
458	C₂×D₄	—	4	64	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	—	4	4	no	—
462	C₂×D₄	—	4	4	no	—
463	C₂×D₄	—	4	4	no	—
464	C₂×D₄	—	4	4	no	—
465	C₂×D₄	—	4	4	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	8	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	8	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	4	8	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	complemented
482	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	complemented
483	C₄⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	32	no	—
485	C₂²⋊C₄	—	2	16	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	4	16	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	complemented
494	C₂³	—	2	4	no	—
495	C₂³	—	2	8	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	16	no	—
498	C₂³	—	2	32	no	—
499	C₂³	—	2	16	no	—
500	C₂³	—	2	8	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	4	no	—
507	C₂³	—	4	4	no	—
508	C₂³	—	4	8	no	—
509	C₂³	—	4	8	no	—
510	C₂³	—	4	4	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	4	no	—
513	C₂³	—	4	8	no	—
514	C₂³	—	4	8	no	—
515	C₂³	—	4	16	no	—
516	C₂³	—	4	16	no	—
517	C₂³	—	4	16	no	—
518	C₂³	—	4	8	no	—
519	C₂³	—	4	32	no	—
520	C₂³	—	4	32	no	—
521	C₂³	—	4	16	no	—
522	C₂³	—	4	16	no	—
523	C₂³	—	4	8	no	—
524	C₂³	—	4	8	no	—
525	C₂³	—	4	16	no	—
526	C₂³	—	4	32	no	—
527	C₂³	—	4	16	no	—
528	C₂³	—	4	8	no	—
529	C₂³	—	4	4	no	—
530	C₂³	—	4	4	no	—
531	C₂³	—	4	8	no	—
532	C₂³	—	4	2	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	4	4	no	—
536	C₂³	—	4	4	no	—
537	C₂³	—	4	8	no	—
538	C₂³	—	8	4	no	—
539	C₂³	—	8	8	no	—
540	C₂³	C₁₉×#120	1	2	yes	—
541	C₂³	C₁₉×#120	1	4	yes	—
542	C₂³	C₁₉×#120	1	1	yes	characteristic
543	C₂³	C₁₉×#120	1	4	yes	—
544	C₂³	C₁₉×#120	1	1	yes	characteristic
545	C₂³	C₁₉×#121	1	4	yes	—
546	C₂³	C₁₉×#121	1	2	yes	—
547	C₂³	C₁₉×#121	1	4	yes	—
548	C₂³	C₁₉×#121	1	2	yes	—
549	C₂³	C₁₉×#127	1	2	yes	—
550	C₂³	C₁₉×#127	1	2	yes	—
551	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
552	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
553	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
554	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
555	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
556	D₄	—	4	64	no	—
557	D₄	—	4	8	no	—
558	D₄	—	4	8	no	—
559	D₄	—	4	4	no	—
560	D₄	—	4	4	no	—
561	D₄	—	4	4	no	—
562	D₄	—	4	4	no	—
563	D₄	—	8	8	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	4	8	no	—
570	C₂×C₄	—	4	16	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	—	8	4	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	4	no	—
583	C₂²	—	2	8	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	2	4	no	—
586	C₂²	—	2	8	no	—
587	C₂²	—	2	16	no	—
588	C₂²	—	2	8	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	8	no	—
597	C₂²	—	4	8	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	32	no	—
600	C₂²	—	4	16	no	—
601	C₂²	—	4	16	no	—
602	C₂²	—	4	8	no	—
603	C₂²	—	4	8	no	—
604	C₂²	—	4	16	no	—
605	C₂²	—	4	4	no	—
606	C₂²	—	4	8	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	8	4	no	—
609	C₂²	—	8	8	no	—
610	C₂²	—	8	8	no	—
611	C₂²	C₁₉×#392	1	4	yes	—
612	C₂²	C₁₉×#392	1	2	yes	—
613	C₂²	C₁₉×#392	1	2	yes	—
614	C₂²	C₁₉×B(4,𝔽₂)	1	4	yes	—
615	C₂²	C₂×C₁₉×#120	1	2	yes	—
616	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
617	C₂²	C₂×C₁₉×#121	1	2	yes	—
618	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
619	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
620	C₄	—	4	8	no	—
621	C₄	—	4	4	no	—
622	C₄	—	4	4	no	—
623	C₄	—	8	2	no	—
624	C₂	—	2	2	no	—
625	C₂	—	2	1	no	—
626	C₂	—	2	1	no	—
627	C₂	—	2	4	no	—
628	C₂	—	2	2	no	—
629	C₂	—	2	2	no	—
630	C₂	—	4	8	no	—
631	C₂	—	8	4	no	—
632	C₂	C₁₉×#2021	1	4	yes	direct product factor
633	C₂	C₂×C₁₉×#392	1	1	yes	characteristic
634	C₂	C₂×C₁₉×B(4,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#534	C₂	semidirect
2. C₂²×C₁₉×#120	C₂	semidirect
3. C₂²×C₁₉×#99	C₂	semidirect
4. C₂×C₁₉×#379	C₂	semidirect
5. C₁₉×#2021	C₂	direct (N × H)
6. C₂×C₁₉×#342	C₂	semidirect
12. C₁₉×#534	C₂²	semidirect
19. C₂×C₁₉×#120	C₂²	semidirect
26. C₂×C₁₉×#99	C₂²	semidirect
28. C₁₉×#379	C₂²	semidirect
29. C₁₉×#342	C₂²	semidirect
37. C₂⁵×C₁₉	D₄	semidirect
38. C₂⁵×C₁₉	D₄	semidirect
53. C₂²×D₄×C₁₉	D₄	semidirect
57. C₂³×C₄×C₁₉	D₄	semidirect
58. C₂³×C₄×C₁₉	D₄	semidirect
80. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
81. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
123. C₂⁴×C₁₉	C₂×D₄	semidirect
124. C₂⁴×C₁₉	C₂×D₄	semidirect
163. C₂²×C₄×C₁₉	C₂×D₄	semidirect
164. C₂²×C₄×C₁₉	C₂×D₄	semidirect
175. C₂²⋊C₄×C₁₉	C₂×D₄	semidirect
176. C₂×#2021	C₁₉	direct (N × H)
262. C₂×#534	C₂×C₁₉	semidirect
263. C₂²×#120	C₂×C₁₉	semidirect
264. C₂²×#99	C₂×C₁₉	semidirect
265. C₂×#379	C₂×C₁₉	semidirect
266. #2021	C₂×C₁₉	direct (N × H)
267. C₂×#342	C₂×C₁₉	semidirect
318. #534	C₂²×C₁₉	semidirect
325. C₂×#120	C₂²×C₁₉	semidirect
332. C₂×#99	C₂²×C₁₉	semidirect
334. #379	C₂²×C₁₉	semidirect
335. #342	C₂²×C₁₉	semidirect
344. C₂×C₁₉	#2021	direct (N × H)
354. C₂⁵	D₄×C₁₉	semidirect
355. C₂⁵	D₄×C₁₉	semidirect
370. C₂²×D₄	D₄×C₁₉	semidirect
374. C₂³×C₄	D₄×C₁₉	semidirect
375. C₂³×C₄	D₄×C₁₉	semidirect
397. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
398. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
403. C₁₉	C₂×#2021	direct (N × H)
441. C₂⁴	C₂×D₄×C₁₉	semidirect
442. C₂⁴	C₂×D₄×C₁₉	semidirect
481. C₂²×C₄	C₂×D₄×C₁₉	semidirect
482. C₂²×C₄	C₂×D₄×C₁₉	semidirect
493. C₂²⋊C₄	C₂×D₄×C₁₉	semidirect
632. C₂	C₁₉×#2021	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#534	2
C₂²×C₁₉×#120	2
C₂²×C₁₉×#99	2
C₂×C₁₉×#379	2
C₁₉×#2021	2
C₂×C₁₉×#342	2
C₂×#2021	19

Subgroups — C2×C19×#2021 #18029400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2021 #18029400