Subgroups — C₂×C₁₉×#2200 #18039507

Order 4864.

1328 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#560	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#458	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×B(4,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#453	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2200	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#353	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#352	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
11	C₁₉×#560	—	2	2	no	—
12	C₁₉×#560	—	2	2	no	—
13	C₁₉×#560	—	2	2	no	—
14	C₁₉×#560	C₂²	1	4	yes	complemented
15	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#126	—	2	1	no	—
17	C₂×C₁₉×#123	—	2	1	no	—
18	C₂×C₁₉×#123	—	2	1	no	—
19	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#121	—	2	1	no	—
21	C₂×C₁₉×#121	—	2	1	no	—
22	C₂×C₁₉×#121	—	2	1	no	—
23	C₂×C₁₉×#120	—	2	1	no	—
24	C₂×C₁₉×#120	—	2	1	no	—
25	C₂×C₁₉×#120	C₂²	1	1	yes	characteristic
26	C₁₉×#458	—	2	2	no	—
27	C₁₉×#458	C₂²	1	4	yes	complemented
28	C₁₉×B(4,𝔽₂)	—	2	2	no	—
29	C₁₉×B(4,𝔽₂)	C₂²	1	4	yes	complemented
30	C₁₉×#453	—	2	2	no	—
31	C₁₉×#453	C₂²	1	4	yes	complemented
32	C₂×C₁₉×#104	—	2	1	no	—
33	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#99	—	2	1	no	—
35	C₂×C₁₉×#99	—	2	1	no	—
36	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic
38	C₁₉×#353	C₂²	1	4	yes	complemented
39	C₁₉×#352	C₂²	1	4	yes	complemented
40	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	4	yes	complemented
41	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
42	C₁₉×H(5,𝔽₂)	—	2	1	no	—
43	C₁₉×H(5,𝔽₂)	—	2	1	no	—
44	C₁₉×H(5,𝔽₂)	—	2	1	no	—
45	C₁₉×H(5,𝔽₂)	—	4	2	no	—
46	C₁₉×H(5,𝔽₂)	C₂³	1	2	yes	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	—	4	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	—	4	1	no	—
57	C₂²×D₄×C₁₉	—	4	1	no	—
58	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	—	2	1	no	—
61	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
62	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
63	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
64	C₂×SD₁₆×C₁₉	—	4	1	no	—
65	C₂×D₈×C₁₉	—	4	1	no	—
66	C₂×M₁₆×C₁₉	—	2	1	no	—
67	C₁₉×#127	—	2	1	no	—
68	C₁₉×#127	—	2	1	no	—
69	C₁₉×#127	D₄	1	2	yes	complemented
70	C₁₉×#127	C₂³	1	2	yes	—
71	C₁₉×#126	—	2	4	no	—
72	C₁₉×#126	—	2	4	no	—
73	C₁₉×#123	—	2	4	no	—
74	C₁₉×#123	—	2	1	no	—
75	C₁₉×#123	—	2	1	no	—
76	C₁₉×#123	—	2	4	no	—
77	C₁₉×#123	—	2	4	no	—
78	C₁₉×#123	—	4	2	no	—
79	C₁₉×#123	D₄	1	2	yes	complemented
80	C₁₉×#123	C₂³	1	2	yes	—
81	C₁₉×#121	—	2	4	no	—
82	C₁₉×#121	—	2	4	no	—
83	C₁₉×#121	—	2	4	no	—
84	C₁₉×#121	—	2	4	no	—
85	C₁₉×#121	—	2	4	no	—
86	C₁₉×#121	—	2	4	no	—
87	C₁₉×#120	—	2	4	no	—
88	C₁₉×#120	—	2	4	no	—
89	C₁₉×#120	—	2	1	no	—
90	C₁₉×#120	—	2	1	no	—
91	C₁₉×#120	—	2	4	no	—
92	C₁₉×#120	—	4	2	no	—
93	C₁₉×#120	D₄	1	2	yes	—
94	C₁₉×#120	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
110	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic, complemented
111	C₁₉×#104	—	2	4	no	—
112	C₁₉×#100	—	2	1	no	—
113	C₁₉×#100	C₂³	1	2	yes	—
114	C₁₉×#99	—	2	1	no	—
115	C₁₉×#99	—	2	1	no	—
116	C₁₉×#99	—	2	4	no	—
117	C₁₉×#99	—	2	4	no	—
118	C₁₉×#99	C₂³	1	2	yes	—
119	C₁₉×#99	C₂³	1	2	yes	—
120	C₂⁴×C₁₉	—	2	1	no	—
121	C₂⁴×C₁₉	—	2	1	no	—
122	C₂⁴×C₁₉	—	2	1	no	—
123	C₂⁴×C₁₉	—	2	1	no	—
124	C₂⁴×C₁₉	—	2	1	no	—
125	C₂⁴×C₁₉	—	4	1	no	—
126	C₂⁴×C₁₉	—	4	1	no	—
127	C₂⁴×C₁₉	—	8	2	no	—
128	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
131	#41×C₁₉	—	2	2	no	—
132	#41×C₁₉	—	2	2	no	—
133	#41×C₁₉	—	4	2	no	—
134	#41×C₁₉	—	4	1	no	—
135	#41×C₁₉	—	4	2	no	—
136	#41×C₁₉	—	4	2	no	—
137	#41×C₁₉	—	4	2	no	—
138	#41×C₁₉	—	4	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	4	no	—
146	C₂×D₄×C₁₉	—	2	4	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	4	1	no	—
155	C₂×D₄×C₁₉	—	4	1	no	—
156	C₂×D₄×C₁₉	—	4	1	no	—
157	C₂×D₄×C₁₉	—	4	1	no	—
158	C₂×D₄×C₁₉	—	4	2	no	—
159	C₂×D₄×C₁₉	—	4	2	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	—	4	1	no	—
162	C₂×D₄×C₁₉	—	4	1	no	—
163	C₂×D₄×C₁₉	—	4	1	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	—	4	2	no	—
166	C₂×D₄×C₁₉	—	4	1	no	—
167	C₂×D₄×C₁₉	—	4	1	no	—
168	C₂×D₄×C₁₉	—	4	1	no	—
169	C₂×D₄×C₁₉	—	4	4	no	—
170	C₂×D₄×C₁₉	—	8	2	no	—
171	C₂×D₄×C₁₉	—	8	2	no	—
172	C₂×D₄×C₁₉	—	8	2	no	—
173	C₂×D₄×C₁₉	—	8	2	no	—
174	C₂×D₄×C₁₉	—	8	1	no	—
175	C₂×D₄×C₁₉	—	8	1	no	—
176	C₂×D₄×C₁₉	—	8	4	no	—
177	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	complemented
181	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	2	1	no	—
186	C₂²×C₄×C₁₉	—	2	1	no	—
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	4	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	4	1	no	—
191	C₂²×C₄×C₁₉	—	4	1	no	—
192	C₂²×C₄×C₁₉	—	4	1	no	—
193	C₂²×C₄×C₁₉	—	4	1	no	—
194	C₂²×C₄×C₁₉	—	4	1	no	—
195	C₂²×C₄×C₁₉	—	8	2	no	—
196	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	complemented
198	SD₁₆×C₁₉	—	4	4	no	—
199	D₈×C₁₉	—	4	4	no	—
200	M₁₆×C₁₉	—	2	2	no	—
201	M₁₆×C₁₉	—	4	1	no	—
202	C₂×C₈×C₁₉	—	4	1	no	—
203	C₄⋊C₄×C₁₉	—	2	4	no	—
204	C₄⋊C₄×C₁₉	—	2	4	no	—
205	C₄⋊C₄×C₁₉	—	2	2	no	—
206	C₄⋊C₄×C₁₉	—	2	2	no	—
207	C₄⋊C₄×C₁₉	—	4	4	no	—
208	C₂²⋊C₄×C₁₉	—	2	4	no	—
209	C₂²⋊C₄×C₁₉	—	2	4	no	—
210	C₂²⋊C₄×C₁₉	—	2	4	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	4	4	no	—
220	C₂²⋊C₄×C₁₉	—	4	1	no	—
221	C₂²⋊C₄×C₁₉	—	4	1	no	—
222	C₂²⋊C₄×C₁₉	—	4	4	no	—
223	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
224	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	complemented
225	C₄²×C₁₉	—	2	1	no	—
226	C₄²×C₁₉	C₂×D₄	1	2	yes	complemented
227	C₂×#2200	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	—	2	1	no	—
230	C₂³×C₁₉	—	2	1	no	—
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	—	2	2	no	—
233	C₂³×C₁₉	—	2	2	no	—
234	C₂³×C₁₉	—	2	2	no	—
235	C₂³×C₁₉	—	2	2	no	—
236	C₂³×C₁₉	—	4	2	no	—
237	C₂³×C₁₉	—	4	2	no	—
238	C₂³×C₁₉	—	4	2	no	—
239	C₂³×C₁₉	—	4	2	no	—
240	C₂³×C₁₉	—	4	2	no	—
241	C₂³×C₁₉	—	4	2	no	—
242	C₂³×C₁₉	—	4	2	no	—
243	C₂³×C₁₉	—	4	1	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	4	no	—
246	C₂³×C₁₉	—	4	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	8	1	no	—
252	C₂³×C₁₉	—	8	2	no	—
253	C₂³×C₁₉	—	8	2	no	—
254	C₂³×C₁₉	—	8	2	no	—
255	C₂³×C₁₉	—	8	4	no	—
256	C₂³×C₁₉	—	8	2	no	—
257	C₂³×C₁₉	—	8	2	no	—
258	C₂³×C₁₉	#120	1	1	yes	characteristic
259	C₂³×C₁₉	#120	1	1	yes	characteristic
260	C₂³×C₁₉	#120	1	1	yes	characteristic
261	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
262	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	Q₈×C₁₉	—	2	2	no	—
264	Q₈×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	2	2	no	—
266	D₄×C₁₉	—	4	1	no	—
267	D₄×C₁₉	—	4	1	no	—
268	D₄×C₁₉	—	4	1	no	—
269	D₄×C₁₉	—	4	1	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	4	1	no	—
272	D₄×C₁₉	—	4	2	no	—
273	D₄×C₁₉	—	4	2	no	—
274	D₄×C₁₉	—	4	2	no	—
275	D₄×C₁₉	—	4	2	no	—
276	D₄×C₁₉	—	4	2	no	—
277	D₄×C₁₉	—	4	2	no	—
278	D₄×C₁₉	—	8	1	no	—
279	D₄×C₁₉	—	8	2	no	—
280	D₄×C₁₉	—	8	2	no	—
281	D₄×C₁₉	—	8	4	no	—
282	D₄×C₁₉	—	8	2	no	—
283	D₄×C₁₉	—	8	2	no	—
284	D₄×C₁₉	—	8	2	no	—
285	D₄×C₁₉	—	8	2	no	—
286	D₄×C₁₉	—	8	4	no	—
287	D₄×C₁₉	—	8	8	no	—
288	C₂×C₄×C₁₉	—	2	1	no	—
289	C₂×C₄×C₁₉	—	2	1	no	—
290	C₂×C₄×C₁₉	—	2	2	no	—
291	C₂×C₄×C₁₉	—	2	2	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	2	2	no	—
295	C₂×C₄×C₁₉	—	2	2	no	—
296	C₂×C₄×C₁₉	—	4	2	no	—
297	C₂×C₄×C₁₉	—	4	2	no	—
298	C₂×C₄×C₁₉	—	4	2	no	—
299	C₂×C₄×C₁₉	—	4	2	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	—	4	2	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	1	no	—
306	C₂×C₄×C₁₉	—	4	2	no	—
307	C₂×C₄×C₁₉	—	4	2	no	—
308	C₂×C₄×C₁₉	—	4	2	no	—
309	C₂×C₄×C₁₉	—	8	1	no	—
310	C₂×C₄×C₁₉	—	8	4	no	—
311	C₂×C₄×C₁₉	—	8	2	no	—
312	C₂×C₄×C₁₉	—	8	2	no	—
313	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
314	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
315	C₈×C₁₉	—	4	2	no	—
316	C₂×#560	C₂×C₁₉	1	1	yes	characteristic, complemented
317	C₂×#458	C₂×C₁₉	1	1	yes	characteristic, complemented
318	C₂×B(4,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
319	C₂×#453	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#2200	C₂×C₁₉	1	8	yes	direct product factor
321	C₂×#353	C₂×C₁₉	1	1	yes	characteristic, complemented
322	C₂×#352	C₂×C₁₉	1	1	yes	characteristic, complemented
323	C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	1	1	yes	characteristic, complemented
324	C₂²×C₁₉	—	2	2	no	—
325	C₂²×C₁₉	—	2	1	no	—
326	C₂²×C₁₉	—	2	1	no	—
327	C₂²×C₁₉	—	2	1	no	—
328	C₂²×C₁₉	—	2	1	no	—
329	C₂²×C₁₉	—	4	1	no	—
330	C₂²×C₁₉	—	4	1	no	—
331	C₂²×C₁₉	—	4	1	no	—
332	C₂²×C₁₉	—	4	1	no	—
333	C₂²×C₁₉	—	4	2	no	—
334	C₂²×C₁₉	—	4	2	no	—
335	C₂²×C₁₉	—	4	2	no	—
336	C₂²×C₁₉	—	4	2	no	—
337	C₂²×C₁₉	—	4	2	no	—
338	C₂²×C₁₉	—	4	2	no	—
339	C₂²×C₁₉	—	4	4	no	—
340	C₂²×C₁₉	—	4	2	no	—
341	C₂²×C₁₉	—	4	2	no	—
342	C₂²×C₁₉	—	4	2	no	—
343	C₂²×C₁₉	—	8	1	no	—
344	C₂²×C₁₉	—	8	1	no	—
345	C₂²×C₁₉	—	8	2	no	—
346	C₂²×C₁₉	—	8	2	no	—
347	C₂²×C₁₉	—	8	2	no	—
348	C₂²×C₁₉	—	8	2	no	—
349	C₂²×C₁₉	—	8	2	no	—
350	C₂²×C₁₉	—	8	4	no	—
351	C₂²×C₁₉	—	8	2	no	—
352	C₂²×C₁₉	—	8	2	no	—
353	C₂²×C₁₉	—	8	2	no	—
354	C₂²×C₁₉	—	16	1	no	—
355	C₂²×C₁₉	—	16	1	no	—
356	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
357	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
358	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
359	C₄×C₁₉	—	2	1	no	—
360	C₄×C₁₉	—	2	1	no	—
361	C₄×C₁₉	—	4	2	no	—
362	C₄×C₁₉	—	4	2	no	—
363	C₄×C₁₉	—	4	2	no	—
364	C₄×C₁₉	—	4	2	no	—
365	C₄×C₁₉	—	4	2	no	—
366	C₄×C₁₉	—	8	2	no	—
367	C₄×C₁₉	—	8	2	no	—
368	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×AGL(1,ℤ/8)	—	2	1	no	—
370	#560	—	2	2	no	—
371	#560	—	2	2	no	—
372	#560	—	2	2	no	—
373	#560	C₂²×C₁₉	1	4	yes	complemented
374	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#126	—	2	1	no	—
376	C₂×#123	—	2	1	no	—
377	C₂×#123	—	2	1	no	—
378	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×#121	—	2	1	no	—
380	C₂×#121	—	2	1	no	—
381	C₂×#121	—	2	1	no	—
382	C₂×#120	—	2	1	no	—
383	C₂×#120	—	2	1	no	—
384	C₂×#120	C₂²×C₁₉	1	1	yes	characteristic
385	#458	—	2	2	no	—
386	#458	C₂²×C₁₉	1	4	yes	complemented
387	B(4,𝔽₂)	—	2	2	no	—
388	B(4,𝔽₂)	C₂²×C₁₉	1	4	yes	complemented
389	#453	—	2	2	no	—
390	#453	C₂²×C₁₉	1	4	yes	complemented
391	C₂×#104	—	2	1	no	—
392	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×#99	—	2	1	no	—
394	C₂×#99	—	2	1	no	—
395	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
396	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
397	#353	C₂²×C₁₉	1	4	yes	complemented
398	#352	C₂²×C₁₉	1	4	yes	complemented
399	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	4	yes	complemented
400	C₂×C₁₉	—	2	1	no	—
401	C₂×C₁₉	—	2	1	no	—
402	C₂×C₁₉	—	4	1	no	—
403	C₂×C₁₉	—	4	1	no	—
404	C₂×C₁₉	—	4	1	no	—
405	C₂×C₁₉	—	4	1	no	—
406	C₂×C₁₉	—	8	2	no	—
407	C₂×C₁₉	—	8	2	no	—
408	C₂×C₁₉	—	8	2	no	—
409	C₂×C₁₉	#2200	1	2	yes	direct product factor
410	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
411	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
412	H(5,𝔽₂)	—	2	1	no	—
413	H(5,𝔽₂)	—	2	1	no	—
414	H(5,𝔽₂)	—	2	1	no	—
415	H(5,𝔽₂)	—	4	2	no	—
416	H(5,𝔽₂)	C₂³×C₁₉	1	2	yes	—
417	C₂×#41	—	2	1	no	—
418	C₂×#41	—	4	1	no	—
419	C₂²×D₄	—	2	1	no	—
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	—	2	1	no	—
423	C₂²×D₄	—	2	1	no	—
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	—	4	1	no	—
427	C₂²×D₄	—	4	1	no	—
428	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
429	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
430	C₂³×C₄	—	2	1	no	—
431	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
432	AGL(1,ℤ/8)	—	2	4	no	—
433	AGL(1,ℤ/8)	—	4	2	no	—
434	C₂×SD₁₆	—	4	1	no	—
435	C₂×D₈	—	4	1	no	—
436	C₂×M₁₆	—	2	1	no	—
437	#127	—	2	1	no	—
438	#127	—	2	1	no	—
439	#127	D₄×C₁₉	1	2	yes	complemented
440	#127	C₂³×C₁₉	1	2	yes	—
441	#126	—	2	4	no	—
442	#126	—	2	4	no	—
443	#123	—	2	4	no	—
444	#123	—	2	1	no	—
445	#123	—	2	1	no	—
446	#123	—	2	4	no	—
447	#123	—	2	4	no	—
448	#123	—	4	2	no	—
449	#123	D₄×C₁₉	1	2	yes	complemented
450	#123	C₂³×C₁₉	1	2	yes	—
451	#121	—	2	4	no	—
452	#121	—	2	4	no	—
453	#121	—	2	4	no	—
454	#121	—	2	4	no	—
455	#121	—	2	4	no	—
456	#121	—	2	4	no	—
457	#120	—	2	4	no	—
458	#120	—	2	4	no	—
459	#120	—	2	1	no	—
460	#120	—	2	1	no	—
461	#120	—	2	4	no	—
462	#120	—	4	2	no	—
463	#120	D₄×C₁₉	1	2	yes	—
464	#120	C₂³×C₁₉	1	2	yes	—
465	C₂×C₄⋊C₄	—	2	1	no	—
466	C₂×C₄⋊C₄	—	2	1	no	—
467	C₂×C₄⋊C₄	—	2	1	no	—
468	C₂×C₄⋊C₄	—	4	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	4	1	no	—
477	C₂×C₂²⋊C₄	—	4	1	no	—
478	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
480	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic, complemented
481	#104	—	2	4	no	—
482	#100	—	2	1	no	—
483	#100	C₂³×C₁₉	1	2	yes	—
484	#99	—	2	1	no	—
485	#99	—	2	1	no	—
486	#99	—	2	4	no	—
487	#99	—	2	4	no	—
488	#99	C₂³×C₁₉	1	2	yes	—
489	#99	C₂³×C₁₉	1	2	yes	—
490	C₁₉	C₂×#2200	1	1	yes	characteristic, direct product factor, Sylow
491	C₂⁴	—	2	1	no	—
492	C₂⁴	—	2	1	no	—
493	C₂⁴	—	2	1	no	—
494	C₂⁴	—	2	1	no	—
495	C₂⁴	—	2	1	no	—
496	C₂⁴	—	4	1	no	—
497	C₂⁴	—	4	1	no	—
498	C₂⁴	—	8	2	no	—
499	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
501	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
502	#41	—	2	2	no	—
503	#41	—	2	2	no	—
504	#41	—	4	2	no	—
505	#41	—	4	1	no	—
506	#41	—	4	2	no	—
507	#41	—	4	2	no	—
508	#41	—	4	2	no	—
509	#41	—	4	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	4	1	no	—
526	C₂×D₄	—	4	1	no	—
527	C₂×D₄	—	4	1	no	—
528	C₂×D₄	—	4	1	no	—
529	C₂×D₄	—	4	2	no	—
530	C₂×D₄	—	4	2	no	—
531	C₂×D₄	—	4	1	no	—
532	C₂×D₄	—	4	1	no	—
533	C₂×D₄	—	4	1	no	—
534	C₂×D₄	—	4	1	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	4	2	no	—
537	C₂×D₄	—	4	1	no	—
538	C₂×D₄	—	4	1	no	—
539	C₂×D₄	—	4	1	no	—
540	C₂×D₄	—	4	4	no	—
541	C₂×D₄	—	8	2	no	—
542	C₂×D₄	—	8	2	no	—
543	C₂×D₄	—	8	2	no	—
544	C₂×D₄	—	8	2	no	—
545	C₂×D₄	—	8	1	no	—
546	C₂×D₄	—	8	1	no	—
547	C₂×D₄	—	8	4	no	—
548	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	complemented
552	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	4	1	no	—
562	C₂²×C₄	—	4	1	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	—	4	1	no	—
566	C₂²×C₄	—	8	2	no	—
567	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	complemented
569	SD₁₆	—	4	4	no	—
570	D₈	—	4	4	no	—
571	M₁₆	—	2	2	no	—
572	M₁₆	—	4	1	no	—
573	C₂×C₈	—	4	1	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	1	no	—
584	C₂²⋊C₄	—	2	1	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	4	4	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₂²⋊C₄	—	4	1	no	—
593	C₂²⋊C₄	—	4	4	no	—
594	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
595	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	complemented
596	C₄²	—	2	1	no	—
597	C₄²	C₂×D₄×C₁₉	1	2	yes	complemented
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	4	2	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	4	2	no	—
611	C₂³	—	4	2	no	—
612	C₂³	—	4	2	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	4	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	8	1	no	—
622	C₂³	—	8	2	no	—
623	C₂³	—	8	2	no	—
624	C₂³	—	8	2	no	—
625	C₂³	—	8	4	no	—
626	C₂³	—	8	2	no	—
627	C₂³	—	8	2	no	—
628	C₂³	C₁₉×#120	1	1	yes	characteristic
629	C₂³	C₁₉×#120	1	1	yes	characteristic
630	C₂³	C₁₉×#120	1	1	yes	characteristic
631	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
632	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
633	Q₈	—	2	2	no	—
634	Q₈	—	4	1	no	—
635	D₄	—	2	2	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	D₄	—	4	1	no	—
639	D₄	—	4	1	no	—
640	D₄	—	4	2	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	2	no	—
643	D₄	—	4	2	no	—
644	D₄	—	4	2	no	—
645	D₄	—	4	2	no	—
646	D₄	—	4	2	no	—
647	D₄	—	4	2	no	—
648	D₄	—	8	1	no	—
649	D₄	—	8	2	no	—
650	D₄	—	8	2	no	—
651	D₄	—	8	4	no	—
652	D₄	—	8	2	no	—
653	D₄	—	8	2	no	—
654	D₄	—	8	2	no	—
655	D₄	—	8	2	no	—
656	D₄	—	8	4	no	—
657	D₄	—	8	8	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	2	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	2	no	—
677	C₂×C₄	—	4	2	no	—
678	C₂×C₄	—	4	2	no	—
679	C₂×C₄	—	8	1	no	—
680	C₂×C₄	—	8	4	no	—
681	C₂×C₄	—	8	2	no	—
682	C₂×C₄	—	8	2	no	—
683	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
685	C₈	—	4	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	—	8	2	no	—
708	C₂²	—	8	2	no	—
709	C₂²	—	8	2	no	—
710	C₂²	—	8	2	no	—
711	C₂²	—	8	2	no	—
712	C₂²	—	8	4	no	—
713	C₂²	—	8	2	no	—
714	C₂²	—	8	2	no	—
715	C₂²	—	8	2	no	—
716	C₂²	—	16	1	no	—
717	C₂²	—	16	1	no	—
718	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
719	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
720	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	8	2	no	—
729	C₄	—	8	2	no	—
730	C₂	—	2	1	no	—
731	C₂	—	2	1	no	—
732	C₂	—	4	1	no	—
733	C₂	—	4	1	no	—
734	C₂	—	4	1	no	—
735	C₂	—	4	1	no	—
736	C₂	—	8	2	no	—
737	C₂	—	8	2	no	—
738	C₂	—	8	2	no	—
739	C₂	C₁₉×#2200	1	2	yes	direct product factor
740	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂⁴×C₁₉
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#560	C₂	semidirect
2. C₂×C₁₉×#458	C₂	semidirect
3. C₂×C₁₉×B(4,𝔽₂)	C₂	semidirect
4. C₂×C₁₉×#453	C₂	semidirect
5. C₁₉×#2200	C₂	direct (N × H)
6. C₂×C₁₉×#353	C₂	semidirect
7. C₂×C₁₉×#352	C₂	semidirect
8. C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	semidirect
14. C₁₉×#560	C₂²	semidirect
27. C₁₉×#458	C₂²	semidirect
29. C₁₉×B(4,𝔽₂)	C₂²	semidirect
31. C₁₉×#453	C₂²	semidirect
38. C₁₉×#353	C₂²	semidirect
39. C₁₉×#352	C₂²	semidirect
40. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
58. C₂²×D₄×C₁₉	D₄	semidirect
61. C₂³×C₄×C₁₉	D₄	semidirect
69. C₁₉×#127	D₄	semidirect
79. C₁₉×#123	D₄	semidirect
109. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
110. C₂×C₄²×C₁₉	D₄	semidirect
180. C₂×D₄×C₁₉	C₂×D₄	semidirect
197. C₂²×C₄×C₁₉	C₂×D₄	semidirect
224. C₂²⋊C₄×C₁₉	C₂×D₄	semidirect
226. C₄²×C₁₉	C₂×D₄	semidirect
227. C₂×#2200	C₁₉	direct (N × H)
316. C₂×#560	C₂×C₁₉	semidirect
317. C₂×#458	C₂×C₁₉	semidirect
318. C₂×B(4,𝔽₂)	C₂×C₁₉	semidirect
319. C₂×#453	C₂×C₁₉	semidirect
320. #2200	C₂×C₁₉	direct (N × H)
321. C₂×#353	C₂×C₁₉	semidirect
322. C₂×#352	C₂×C₁₉	semidirect
323. C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	semidirect
373. #560	C₂²×C₁₉	semidirect
386. #458	C₂²×C₁₉	semidirect
388. B(4,𝔽₂)	C₂²×C₁₉	semidirect
390. #453	C₂²×C₁₉	semidirect
397. #353	C₂²×C₁₉	semidirect
398. #352	C₂²×C₁₉	semidirect
399. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
409. C₂×C₁₉	#2200	direct (N × H)
428. C₂²×D₄	D₄×C₁₉	semidirect
431. C₂³×C₄	D₄×C₁₉	semidirect
439. #127	D₄×C₁₉	semidirect
449. #123	D₄×C₁₉	semidirect
479. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
480. C₂×C₄²	D₄×C₁₉	semidirect
490. C₁₉	C₂×#2200	direct (N × H)
551. C₂×D₄	C₂×D₄×C₁₉	semidirect
568. C₂²×C₄	C₂×D₄×C₁₉	semidirect
595. C₂²⋊C₄	C₂×D₄×C₁₉	semidirect
597. C₄²	C₂×D₄×C₁₉	semidirect
739. C₂	C₁₉×#2200	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×#560	2
C₂×C₁₉×#458	2
C₂×C₁₉×B(4,𝔽₂)	2
C₂×C₁₉×#453	2
C₁₉×#2200	2
C₂×C₁₉×#353	2
C₂×C₁₉×#352	2
C₂×C₁₉×AΣL(1,𝔽₁₆)	2
C₂×#2200	19

Subgroups — C2×C19×#2200 #18039507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2200 #18039507