Subgroups — C₂×C₁₉×#2197 #18039503

Order 4864.

1320 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#551	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
4	C₂×C₁₉×#455	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2197	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#354	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×#137	—	2	1	no	—
11	C₁₉×#551	—	2	2	no	—
12	C₁₉×#551	—	2	2	no	—
13	C₁₉×#551	—	2	2	no	—
14	C₁₉×#551	C₂²	1	4	yes	complemented
15	C₂×C₁₉×#126	—	2	1	no	—
16	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
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×C₂²⋊Q₈	—	2	1	no	—
21	C₂×C₁₉×#120	—	2	1	no	—
22	C₂×C₁₉×#120	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	—	2	1	no	—
24	C₂×C₁₉×#117	—	2	1	no	—
25	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—
30	C₁₉×#455	—	2	2	no	—
31	C₁₉×#455	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×#354	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×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
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	—	4	1	no	—
54	C₂²×D₄×C₁₉	—	4	1	no	—
55	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	—	2	1	no	—
58	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
59	C₁₉×#137	—	2	4	no	—
60	C₁₉×#137	—	4	2	no	—
61	C₂×Q₁₆×C₁₉	—	4	1	no	—
62	C₂×SD₁₆×C₁₉	—	4	1	no	—
63	C₂×M₁₆×C₁₉	—	2	1	no	—
64	C₁₉×#126	—	2	4	no	—
65	C₁₉×#126	—	2	4	no	—
66	C₁₉×#124	—	2	1	no	—
67	C₁₉×#124	—	2	1	no	—
68	C₁₉×#124	D₄	1	2	yes	complemented
69	C₁₉×#124	C₂³	1	2	yes	—
70	C₁₉×#123	—	2	4	no	—
71	C₁₉×#123	—	2	1	no	—
72	C₁₉×#123	—	2	1	no	—
73	C₁₉×#123	—	2	4	no	—
74	C₁₉×#123	—	2	4	no	—
75	C₁₉×#123	—	4	2	no	—
76	C₁₉×#123	D₄	1	2	yes	complemented
77	C₁₉×#123	C₂³	1	2	yes	—
78	C₁₉×C₂²⋊Q₈	—	2	4	no	—
79	C₁₉×C₂²⋊Q₈	—	2	4	no	—
80	C₁₉×#120	—	2	1	no	—
81	C₁₉×#120	—	2	1	no	—
82	C₁₉×#120	—	2	4	no	—
83	C₁₉×#120	—	4	2	no	—
84	C₁₉×#120	D₄	1	2	yes	—
85	C₁₉×#120	C₂³	1	2	yes	—
86	C₄×D₄×C₁₉	—	2	4	no	—
87	C₄×D₄×C₁₉	—	2	4	no	—
88	C₁₉×#117	—	2	4	no	—
89	C₁₉×#117	—	2	4	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	4	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	—	4	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
109	C₂×C₄²×C₁₉	—	2	1	no	—
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	—	4	1	no	—
125	C₂⁴×C₁₉	—	4	4	no	—
126	C₂⁴×C₁₉	—	4	1	no	—
127	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
130	#41×C₁₉	—	2	2	no	—
131	#41×C₁₉	—	2	2	no	—
132	#41×C₁₉	—	4	2	no	—
133	#41×C₁₉	—	4	1	no	—
134	#41×C₁₉	—	4	2	no	—
135	#41×C₁₉	—	4	2	no	—
136	#41×C₁₉	—	4	2	no	—
137	#41×C₁₉	—	4	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	4	1	no	—
141	C₂×Q₈×C₁₉	—	4	1	no	—
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	complemented
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	2	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	—	4	1	no	—
151	C₂×D₄×C₁₉	—	4	1	no	—
152	C₂×D₄×C₁₉	—	4	2	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	4	4	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	1	no	—
159	C₂×D₄×C₁₉	—	4	2	no	—
160	C₂×D₄×C₁₉	—	4	2	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	4	no	—
165	C₂×D₄×C₁₉	—	8	4	no	—
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	—	2	4	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	4	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	4	1	no	—
181	C₂²×C₄×C₁₉	—	4	4	no	—
182	C₂²×C₄×C₁₉	—	4	1	no	—
183	C₂²×C₄×C₁₉	—	4	1	no	—
184	C₂²×C₄×C₁₉	—	4	1	no	—
185	C₂²×C₄×C₁₉	—	4	1	no	—
186	C₂²×C₄×C₁₉	—	8	1	no	—
187	C₂²×C₄×C₁₉	—	8	1	no	—
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	complemented
190	Q₁₆×C₁₉	—	4	4	no	—
191	SD₁₆×C₁₉	—	4	4	no	—
192	M₁₆×C₁₉	—	2	2	no	—
193	M₁₆×C₁₉	—	4	1	no	—
194	C₂×C₈×C₁₉	—	4	1	no	—
195	C₄⋊C₄×C₁₉	—	2	4	no	—
196	C₄⋊C₄×C₁₉	—	2	4	no	—
197	C₄⋊C₄×C₁₉	—	2	4	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	4	4	no	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	2	4	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	4	4	no	—
216	C₂²⋊C₄×C₁₉	—	4	1	no	—
217	C₂²⋊C₄×C₁₉	—	4	1	no	—
218	C₂²⋊C₄×C₁₉	—	4	4	no	—
219	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
220	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	complemented
221	C₄²×C₁₉	—	2	4	no	—
222	C₄²×C₁₉	—	2	1	no	—
223	C₄²×C₁₉	C₂×D₄	1	2	yes	complemented
224	C₂×#2197	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂³×C₁₉	—	2	4	no	—
226	C₂³×C₁₉	—	2	2	no	—
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	—	2	1	no	—
230	C₂³×C₁₉	—	2	1	no	—
231	C₂³×C₁₉	—	2	2	no	—
232	C₂³×C₁₉	—	2	2	no	—
233	C₂³×C₁₉	—	4	2	no	—
234	C₂³×C₁₉	—	4	2	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	—	4	2	no	—
237	C₂³×C₁₉	—	4	4	no	—
238	C₂³×C₁₉	—	4	4	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	—	4	1	no	—
243	C₂³×C₁₉	—	4	4	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	8	1	no	—
246	C₂³×C₁₉	—	8	4	no	—
247	C₂³×C₁₉	—	8	2	no	—
248	C₂³×C₁₉	—	8	2	no	—
249	C₂³×C₁₉	—	8	2	no	—
250	C₂³×C₁₉	#120	1	1	yes	characteristic
251	C₂³×C₁₉	#120	1	1	yes	characteristic
252	C₂³×C₁₉	#120	1	1	yes	characteristic
253	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
254	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	Q₈×C₁₉	—	2	2	no	—
256	Q₈×C₁₉	—	4	2	no	—
257	Q₈×C₁₉	—	4	1	no	—
258	Q₈×C₁₉	—	8	1	no	—
259	D₄×C₁₉	—	2	2	no	—
260	D₄×C₁₉	—	4	1	no	—
261	D₄×C₁₉	—	4	1	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	4	4	no	—
266	D₄×C₁₉	—	4	4	no	—
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	4	2	no	—
269	D₄×C₁₉	—	4	2	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	4	2	no	—
272	D₄×C₁₉	—	4	2	no	—
273	D₄×C₁₉	—	8	8	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	2	no	—
278	C₂×C₄×C₁₉	—	2	2	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	2	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	4	2	no	—
284	C₂×C₄×C₁₉	—	4	2	no	—
285	C₂×C₄×C₁₉	—	4	2	no	—
286	C₂×C₄×C₁₉	—	4	2	no	—
287	C₂×C₄×C₁₉	—	4	8	no	—
288	C₂×C₄×C₁₉	—	4	2	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	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	—	8	1	no	—
300	C₂×C₄×C₁₉	—	8	4	no	—
301	C₂×C₄×C₁₉	—	8	2	no	—
302	C₂×C₄×C₁₉	—	8	2	no	—
303	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
304	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
305	C₈×C₁₉	—	4	2	no	—
306	C₂×#551	C₂×C₁₉	1	1	yes	characteristic, complemented
307	C₂×#458	C₂×C₁₉	1	1	yes	characteristic, complemented
308	C₂×B(4,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
309	C₂×#455	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#2197	C₂×C₁₉	1	8	yes	direct product factor
311	C₂×#354	C₂×C₁₉	1	1	yes	characteristic, complemented
312	C₂×#352	C₂×C₁₉	1	1	yes	characteristic, complemented
313	C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	1	1	yes	characteristic, complemented
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	—	2	4	no	—
316	C₂²×C₁₉	—	2	1	no	—
317	C₂²×C₁₉	—	2	1	no	—
318	C₂²×C₁₉	—	2	1	no	—
319	C₂²×C₁₉	—	2	1	no	—
320	C₂²×C₁₉	—	4	1	no	—
321	C₂²×C₁₉	—	4	1	no	—
322	C₂²×C₁₉	—	4	1	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	4	4	no	—
326	C₂²×C₁₉	—	4	4	no	—
327	C₂²×C₁₉	—	4	2	no	—
328	C₂²×C₁₉	—	4	2	no	—
329	C₂²×C₁₉	—	4	4	no	—
330	C₂²×C₁₉	—	4	2	no	—
331	C₂²×C₁₉	—	4	2	no	—
332	C₂²×C₁₉	—	8	1	no	—
333	C₂²×C₁₉	—	8	1	no	—
334	C₂²×C₁₉	—	8	2	no	—
335	C₂²×C₁₉	—	8	4	no	—
336	C₂²×C₁₉	—	8	2	no	—
337	C₂²×C₁₉	—	8	2	no	—
338	C₂²×C₁₉	—	8	2	no	—
339	C₂²×C₁₉	—	16	1	no	—
340	C₂²×C₁₉	—	16	1	no	—
341	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
342	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
343	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
344	C₄×C₁₉	—	2	1	no	—
345	C₄×C₁₉	—	2	1	no	—
346	C₄×C₁₉	—	4	2	no	—
347	C₄×C₁₉	—	4	2	no	—
348	C₄×C₁₉	—	4	2	no	—
349	C₄×C₁₉	—	4	2	no	—
350	C₄×C₁₉	—	4	2	no	—
351	C₄×C₁₉	—	4	2	no	—
352	C₄×C₁₉	—	8	2	no	—
353	C₄×C₁₉	—	8	2	no	—
354	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×#137	—	2	1	no	—
356	#551	—	2	2	no	—
357	#551	—	2	2	no	—
358	#551	—	2	2	no	—
359	#551	C₂²×C₁₉	1	4	yes	complemented
360	C₂×#126	—	2	1	no	—
361	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#123	—	2	1	no	—
363	C₂×#123	—	2	1	no	—
364	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×C₂²⋊Q₈	—	2	1	no	—
366	C₂×#120	—	2	1	no	—
367	C₂×#120	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×C₄×D₄	—	2	1	no	—
369	C₂×#117	—	2	1	no	—
370	C₂²×C₂²⋊C₄	—	2	1	no	—
371	#458	—	2	2	no	—
372	#458	C₂²×C₁₉	1	4	yes	complemented
373	B(4,𝔽₂)	—	2	2	no	—
374	B(4,𝔽₂)	C₂²×C₁₉	1	4	yes	—
375	#455	—	2	2	no	—
376	#455	C₂²×C₁₉	1	4	yes	complemented
377	C₂×#104	—	2	1	no	—
378	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×#99	—	2	1	no	—
380	C₂×#99	—	2	1	no	—
381	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
383	#354	C₂²×C₁₉	1	4	yes	complemented
384	#352	C₂²×C₁₉	1	4	yes	complemented
385	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	4	yes	complemented
386	C₂×C₁₉	—	2	1	no	—
387	C₂×C₁₉	—	2	1	no	—
388	C₂×C₁₉	—	4	1	no	—
389	C₂×C₁₉	—	4	1	no	—
390	C₂×C₁₉	—	4	4	no	—
391	C₂×C₁₉	—	4	1	no	—
392	C₂×C₁₉	—	4	1	no	—
393	C₂×C₁₉	—	8	2	no	—
394	C₂×C₁₉	#2197	1	2	yes	direct product factor
395	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
396	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
397	H(5,𝔽₂)	—	2	1	no	—
398	H(5,𝔽₂)	—	2	1	no	—
399	H(5,𝔽₂)	—	2	1	no	—
400	H(5,𝔽₂)	—	4	2	no	—
401	H(5,𝔽₂)	C₂³×C₁₉	1	2	yes	—
402	C₂×#41	—	2	1	no	—
403	C₂×#41	—	4	1	no	—
404	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
405	C₂²×D₄	—	2	1	no	—
406	C₂²×D₄	—	2	1	no	—
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	—	4	1	no	—
409	C₂²×D₄	—	4	1	no	—
410	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
411	C₂³×C₄	—	2	1	no	—
412	C₂³×C₄	—	2	1	no	—
413	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
414	#137	—	2	4	no	—
415	#137	—	4	2	no	—
416	C₂×Q₁₆	—	4	1	no	—
417	C₂×SD₁₆	—	4	1	no	—
418	C₂×M₁₆	—	2	1	no	—
419	#126	—	2	4	no	—
420	#126	—	2	4	no	—
421	#124	—	2	1	no	—
422	#124	—	2	1	no	—
423	#124	D₄×C₁₉	1	2	yes	complemented
424	#124	C₂³×C₁₉	1	2	yes	—
425	#123	—	2	4	no	—
426	#123	—	2	1	no	—
427	#123	—	2	1	no	—
428	#123	—	2	4	no	—
429	#123	—	2	4	no	—
430	#123	—	4	2	no	—
431	#123	D₄×C₁₉	1	2	yes	complemented
432	#123	C₂³×C₁₉	1	2	yes	—
433	C₂²⋊Q₈	—	2	4	no	—
434	C₂²⋊Q₈	—	2	4	no	—
435	#120	—	2	1	no	—
436	#120	—	2	1	no	—
437	#120	—	2	4	no	—
438	#120	—	4	2	no	—
439	#120	D₄×C₁₉	1	2	yes	—
440	#120	C₂³×C₁₉	1	2	yes	—
441	C₄×D₄	—	2	4	no	—
442	C₄×D₄	—	2	4	no	—
443	#117	—	2	4	no	—
444	#117	—	2	4	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	4	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	4	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	4	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	4	1	no	—
461	C₂×C₂²⋊C₄	—	4	1	no	—
462	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
464	C₂×C₄²	—	2	1	no	—
465	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic, complemented
466	#104	—	2	4	no	—
467	#100	—	2	1	no	—
468	#100	C₂³×C₁₉	1	2	yes	—
469	#99	—	2	1	no	—
470	#99	—	2	1	no	—
471	#99	—	2	4	no	—
472	#99	—	2	4	no	—
473	#99	C₂³×C₁₉	1	2	yes	—
474	#99	C₂³×C₁₉	1	2	yes	—
475	C₁₉	C₂×#2197	1	1	yes	characteristic, direct product factor, Sylow
476	C₂⁴	—	2	1	no	—
477	C₂⁴	—	2	1	no	—
478	C₂⁴	—	2	1	no	—
479	C₂⁴	—	2	1	no	—
480	C₂⁴	—	4	1	no	—
481	C₂⁴	—	4	4	no	—
482	C₂⁴	—	4	1	no	—
483	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
486	#41	—	2	2	no	—
487	#41	—	2	2	no	—
488	#41	—	4	2	no	—
489	#41	—	4	1	no	—
490	#41	—	4	2	no	—
491	#41	—	4	2	no	—
492	#41	—	4	2	no	—
493	#41	—	4	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	4	1	no	—
497	C₂×Q₈	—	4	1	no	—
498	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	complemented
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	4	1	no	—
507	C₂×D₄	—	4	1	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	—	4	4	no	—
511	C₂×D₄	—	4	1	no	—
512	C₂×D₄	—	4	1	no	—
513	C₂×D₄	—	4	1	no	—
514	C₂×D₄	—	4	1	no	—
515	C₂×D₄	—	4	2	no	—
516	C₂×D₄	—	4	2	no	—
517	C₂×D₄	—	4	1	no	—
518	C₂×D₄	—	4	1	no	—
519	C₂×D₄	—	4	1	no	—
520	C₂×D₄	—	4	4	no	—
521	C₂×D₄	—	8	4	no	—
522	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	4	1	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	1	no	—
539	C₂²×C₄	—	4	1	no	—
540	C₂²×C₄	—	4	1	no	—
541	C₂²×C₄	—	4	1	no	—
542	C₂²×C₄	—	8	1	no	—
543	C₂²×C₄	—	8	1	no	—
544	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	complemented
546	Q₁₆	—	4	4	no	—
547	SD₁₆	—	4	4	no	—
548	M₁₆	—	2	2	no	—
549	M₁₆	—	4	1	no	—
550	C₂×C₈	—	4	1	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	4	4	no	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	1	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	4	4	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	—	4	4	no	—
575	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
576	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	complemented
577	C₄²	—	2	4	no	—
578	C₄²	—	2	1	no	—
579	C₄²	C₂×D₄×C₁₉	1	2	yes	complemented
580	C₂³	—	2	4	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	4	2	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	4	2	no	—
591	C₂³	—	4	2	no	—
592	C₂³	—	4	4	no	—
593	C₂³	—	4	4	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	4	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	8	1	no	—
601	C₂³	—	8	4	no	—
602	C₂³	—	8	2	no	—
603	C₂³	—	8	2	no	—
604	C₂³	—	8	2	no	—
605	C₂³	C₁₉×#120	1	1	yes	characteristic
606	C₂³	C₁₉×#120	1	1	yes	characteristic
607	C₂³	C₁₉×#120	1	1	yes	characteristic
608	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
609	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
610	Q₈	—	2	2	no	—
611	Q₈	—	4	2	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	8	1	no	—
614	D₄	—	2	2	no	—
615	D₄	—	4	1	no	—
616	D₄	—	4	1	no	—
617	D₄	—	4	1	no	—
618	D₄	—	4	1	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	2	no	—
621	D₄	—	4	2	no	—
622	D₄	—	4	2	no	—
623	D₄	—	4	2	no	—
624	D₄	—	4	4	no	—
625	D₄	—	4	4	no	—
626	D₄	—	4	2	no	—
627	D₄	—	4	2	no	—
628	D₄	—	8	8	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	8	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	—	8	1	no	—
655	C₂×C₄	—	8	4	no	—
656	C₂×C₄	—	8	2	no	—
657	C₂×C₄	—	8	2	no	—
658	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
660	C₈	—	4	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	4	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	8	2	no	—
682	C₂²	—	8	4	no	—
683	C₂²	—	8	2	no	—
684	C₂²	—	8	2	no	—
685	C₂²	—	8	2	no	—
686	C₂²	—	16	1	no	—
687	C₂²	—	16	1	no	—
688	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
689	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
690	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	8	2	no	—
700	C₄	—	8	2	no	—
701	C₂	—	2	1	no	—
702	C₂	—	2	1	no	—
703	C₂	—	4	1	no	—
704	C₂	—	4	1	no	—
705	C₂	—	4	4	no	—
706	C₂	—	4	1	no	—
707	C₂	—	4	1	no	—
708	C₂	—	8	2	no	—
709	C₂	C₁₉×#2197	1	2	yes	direct product factor
710	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
prime radical	C₂×C₁₉×B(4,𝔽₂)	C₂
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×#551	C₂	semidirect
2. C₂×C₁₉×#458	C₂	semidirect
4. C₂×C₁₉×#455	C₂	semidirect
5. C₁₉×#2197	C₂	direct (N × H)
6. C₂×C₁₉×#354	C₂	semidirect
7. C₂×C₁₉×#352	C₂	semidirect
8. C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	semidirect
14. C₁₉×#551	C₂²	semidirect
27. C₁₉×#458	C₂²	semidirect
31. C₁₉×#455	C₂²	semidirect
38. C₁₉×#354	C₂²	semidirect
39. C₁₉×#352	C₂²	semidirect
40. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
49. C₂²×Q₈×C₁₉	D₄	semidirect
58. C₂³×C₄×C₁₉	D₄	semidirect
68. C₁₉×#124	D₄	semidirect
76. C₁₉×#123	D₄	semidirect
108. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
110. C₂×C₄²×C₁₉	D₄	semidirect
142. C₂×Q₈×C₁₉	C₂×D₄	semidirect
189. C₂²×C₄×C₁₉	C₂×D₄	semidirect
220. C₂²⋊C₄×C₁₉	C₂×D₄	semidirect
223. C₄²×C₁₉	C₂×D₄	semidirect
224. C₂×#2197	C₁₉	direct (N × H)
306. C₂×#551	C₂×C₁₉	semidirect
307. C₂×#458	C₂×C₁₉	semidirect
309. C₂×#455	C₂×C₁₉	semidirect
310. #2197	C₂×C₁₉	direct (N × H)
311. C₂×#354	C₂×C₁₉	semidirect
312. C₂×#352	C₂×C₁₉	semidirect
313. C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	semidirect
359. #551	C₂²×C₁₉	semidirect
372. #458	C₂²×C₁₉	semidirect
376. #455	C₂²×C₁₉	semidirect
383. #354	C₂²×C₁₉	semidirect
384. #352	C₂²×C₁₉	semidirect
385. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
394. C₂×C₁₉	#2197	direct (N × H)
404. C₂²×Q₈	D₄×C₁₉	semidirect
413. C₂³×C₄	D₄×C₁₉	semidirect
423. #124	D₄×C₁₉	semidirect
431. #123	D₄×C₁₉	semidirect
463. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
465. C₂×C₄²	D₄×C₁₉	semidirect
475. C₁₉	C₂×#2197	direct (N × H)
498. C₂×Q₈	C₂×D₄×C₁₉	semidirect
545. C₂²×C₄	C₂×D₄×C₁₉	semidirect
576. C₂²⋊C₄	C₂×D₄×C₁₉	semidirect
579. C₄²	C₂×D₄×C₁₉	semidirect
709. C₂	C₁₉×#2197	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×#551	2
C₂×C₁₉×#458	2
C₂×C₁₉×B(4,𝔽₂)	2
C₂×C₁₉×#455	2
C₁₉×#2197	2
C₂×C₁₉×#354	2
C₂×C₁₉×#352	2
C₂×C₁₉×AΣL(1,𝔽₁₆)	2
C₂×#2197	19

Subgroups — C2×C19×#2197 #18039503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2197 #18039503