Subgroups — C₁₉×#32888 #18038847

Order 4864.

4070 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#453	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3006	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2433	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1792	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1789	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1783	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×H(5,𝔽₂)	—	2	16	no	—
9	C₂×C₁₉×H(5,𝔽₂)	—	2	4	no	—
10	C₂×C₁₉×H(5,𝔽₂)	—	2	2	no	—
11	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	4	yes	—
12	C₂²×#41×C₁₉	—	2	2	no	—
13	C₂²×#41×C₁₉	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₉	—	2	2	no	—
15	C₂³×D₄×C₁₉	—	2	2	no	—
16	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
18	C₂×C₁₉×#127	C₂²	1	2	yes	complemented
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₉×#120	—	2	2	no	—
21	C₁₉×#453	—	2	16	no	—
22	C₁₉×#449	—	2	4	no	—
23	C₁₉×#448	—	2	2	no	—
24	C₁₉×#447	—	2	2	no	—
25	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
26	C₁₉×#417	C₂²	1	4	yes	complemented
27	C₂×C₁₉×#100	C₂²	1	4	yes	complemented
28	C₁₉×#407	C₂²	1	2	yes	complemented
29	C₁₉×#392	—	2	2	no	—
30	C₁₉×#390	C₂²	1	2	yes	complemented
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
32	C₂⁵×C₁₉	—	2	2	no	—
33	C₂⁵×C₁₉	D₄	1	2	yes	—
34	C₁₉×H(5,𝔽₂)	—	2	32	no	—
35	C₁₉×H(5,𝔽₂)	—	2	32	no	—
36	C₁₉×H(5,𝔽₂)	—	2	32	no	—
37	C₁₉×H(5,𝔽₂)	—	2	16	no	—
38	C₁₉×H(5,𝔽₂)	—	2	8	no	—
39	C₁₉×H(5,𝔽₂)	D₄	1	16	yes	complemented
40	C₂×#41×C₁₉	—	2	32	no	—
41	C₂×#41×C₁₉	—	2	8	no	—
42	C₂×#41×C₁₉	—	2	16	no	—
43	C₂×#41×C₁₉	—	2	8	no	—
44	C₂×#41×C₁₉	—	2	2	no	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	D₄	1	4	yes	complemented
47	C₂×#41×C₁₉	C₂³	1	4	yes	—
48	C₂²×Q₈×C₁₉	D₄	1	2	yes	complemented
49	C₂²×D₄×C₁₉	—	2	4	no	—
50	C₂²×D₄×C₁₉	—	2	32	no	—
51	C₂²×D₄×C₁₉	—	2	32	no	—
52	C₂²×D₄×C₁₉	—	2	8	no	—
53	C₂²×D₄×C₁₉	—	2	8	no	—
54	C₂²×D₄×C₁₉	—	2	2	no	—
55	C₂²×D₄×C₁₉	—	2	8	no	—
56	C₂²×D₄×C₁₉	—	2	8	no	—
57	C₂²×D₄×C₁₉	—	2	8	no	—
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	4	no	—
60	C₂²×D₄×C₁₉	—	2	2	no	—
61	C₂²×D₄×C₁₉	—	2	2	no	—
62	C₂²×D₄×C₁₉	D₄	1	2	yes	—
63	C₂²×D₄×C₁₉	D₄	1	2	yes	complemented
64	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
66	C₂³×C₄×C₁₉	—	2	2	no	—
67	C₂³×C₄×C₁₉	—	2	2	no	—
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
70	C₂×SD₁₆×C₁₉	—	2	4	no	—
71	C₂×D₈×C₁₉	—	2	4	no	—
72	C₂×M₁₆×C₁₉	C₂³	1	4	yes	complemented
73	C₁₉×#127	—	2	8	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#120	—	4	8	no	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	C₂³	1	2	yes	complemented
82	C₁₉×#104	—	2	16	no	—
83	C₁₉×#103	—	2	4	no	—
84	C₁₉×#102	—	2	4	no	—
85	C₁₉×#100	—	2	8	no	—
86	C₁₉×C₂²⋊C₈	—	2	2	no	—
87	C₁₉×C₂²⋊C₈	—	2	2	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₂⁴×C₁₉	—	2	16	no	—
90	C₂⁴×C₁₉	—	2	8	no	—
91	C₂⁴×C₁₉	—	2	2	no	—
92	C₂⁴×C₁₉	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	8	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	1	no	—
96	C₂⁴×C₁₉	—	4	4	no	—
97	C₂⁴×C₁₉	—	8	2	no	—
98	C₂⁴×C₁₉	—	8	4	no	—
99	C₂⁴×C₁₉	—	8	4	no	—
100	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
102	#41×C₁₉	—	2	64	no	—
103	#41×C₁₉	—	2	16	no	—
104	#41×C₁₉	—	2	32	no	—
105	#41×C₁₉	—	2	16	no	—
106	#41×C₁₉	—	2	32	no	—
107	#41×C₁₉	—	2	8	no	—
108	#41×C₁₉	—	2	8	no	—
109	#41×C₁₉	—	2	8	no	—
110	#41×C₁₉	C₂×D₄	1	16	yes	—
111	C₂×Q₈×C₁₉	—	2	8	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
114	C₂×D₄×C₁₉	—	2	32	no	—
115	C₂×D₄×C₁₉	—	2	16	no	—
116	C₂×D₄×C₁₉	—	2	16	no	—
117	C₂×D₄×C₁₉	—	2	16	no	—
118	C₂×D₄×C₁₉	—	2	64	no	—
119	C₂×D₄×C₁₉	—	2	64	no	—
120	C₂×D₄×C₁₉	—	2	32	no	—
121	C₂×D₄×C₁₉	—	2	32	no	—
122	C₂×D₄×C₁₉	—	2	16	no	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	32	no	—
125	C₂×D₄×C₁₉	—	2	8	no	—
126	C₂×D₄×C₁₉	—	2	4	no	—
127	C₂×D₄×C₁₉	—	2	8	no	—
128	C₂×D₄×C₁₉	—	2	32	no	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	4	no	—
135	C₂×D₄×C₁₉	—	4	8	no	—
136	C₂×D₄×C₁₉	—	4	4	no	—
137	C₂×D₄×C₁₉	—	4	1	no	—
138	C₂×D₄×C₁₉	—	4	1	no	—
139	C₂×D₄×C₁₉	—	4	8	no	—
140	C₂×D₄×C₁₉	—	8	4	no	—
141	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
142	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₉	—	2	16	no	—
144	C₂²×C₄×C₁₉	—	2	16	no	—
145	C₂²×C₄×C₁₉	—	2	8	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	4	no	—
148	C₂²×C₄×C₁₉	—	2	4	no	—
149	C₂²×C₄×C₁₉	—	2	4	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	SD₁₆×C₁₉	—	4	8	no	—
157	D₈×C₁₉	—	4	8	no	—
158	M₁₆×C₁₉	—	2	8	no	—
159	C₂×C₈×C₁₉	—	2	4	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	2	4	no	—
162	C₂²⋊C₄×C₁₉	—	4	8	no	—
163	C₂²⋊C₄×C₁₉	—	4	2	no	—
164	C₄²×C₁₉	—	2	4	no	—
165	#32888	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	2	8	no	—
167	C₂³×C₁₉	—	2	8	no	—
168	C₂³×C₁₉	—	2	8	no	—
169	C₂³×C₁₉	—	2	32	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	2	4	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	4	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	4	no	—
177	C₂³×C₁₉	—	4	4	no	—
178	C₂³×C₁₉	—	4	4	no	—
179	C₂³×C₁₉	—	4	4	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	—	4	4	no	—
183	C₂³×C₁₉	—	4	4	no	—
184	C₂³×C₁₉	—	4	2	no	—
185	C₂³×C₁₉	—	4	1	no	—
186	C₂³×C₁₉	—	8	2	no	—
187	C₂³×C₁₉	—	8	2	no	—
188	C₂³×C₁₉	—	8	16	no	—
189	C₂³×C₁₉	—	8	32	no	—
190	C₂³×C₁₉	—	8	8	no	—
191	C₂³×C₁₉	—	8	8	no	—
192	C₂³×C₁₉	#120	1	1	yes	characteristic
193	C₂³×C₁₉	#120	1	1	yes	characteristic
194	C₂³×C₁₉	#120	1	8	yes	—
195	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₁₉	—	2	8	no	—
197	Q₈×C₁₉	—	2	4	no	—
198	Q₈×C₁₉	#120	1	8	yes	complemented
199	D₄×C₁₉	—	2	64	no	—
200	D₄×C₁₉	—	2	16	no	—
201	D₄×C₁₉	—	2	16	no	—
202	D₄×C₁₉	—	2	8	no	—
203	D₄×C₁₉	—	2	16	no	—
204	D₄×C₁₉	—	2	16	no	—
205	D₄×C₁₉	—	2	4	no	—
206	D₄×C₁₉	—	4	4	no	—
207	D₄×C₁₉	—	8	16	no	—
208	D₄×C₁₉	—	8	2	no	—
209	D₄×C₁₉	—	8	2	no	—
210	D₄×C₁₉	#120	1	8	yes	complemented
211	C₂×C₄×C₁₉	—	2	8	no	—
212	C₂×C₄×C₁₉	—	2	32	no	—
213	C₂×C₄×C₁₉	—	2	16	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	2	16	no	—
218	C₂×C₄×C₁₉	—	2	4	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	#120	1	2	yes	—
225	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
227	C₈×C₁₉	—	4	4	no	—
228	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
229	C₂×#453	C₂×C₁₉	1	4	yes	complemented
230	#3006	C₂×C₁₉	1	2	yes	complemented
231	#2433	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#1792	C₂×C₁₉	1	4	yes	complemented
233	#1789	C₂×C₁₉	1	2	yes	complemented
234	#1783	C₂×C₁₉	1	1	yes	characteristic, complemented
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	2	8	no	—
241	C₂²×C₁₉	—	2	8	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	4	4	no	—
245	C₂²×C₁₉	—	4	8	no	—
246	C₂²×C₁₉	—	4	16	no	—
247	C₂²×C₁₉	—	4	16	no	—
248	C₂²×C₁₉	—	4	4	no	—
249	C₂²×C₁₉	—	4	4	no	—
250	C₂²×C₁₉	—	4	4	no	—
251	C₂²×C₁₉	—	4	4	no	—
252	C₂²×C₁₉	—	8	4	no	—
253	C₂²×C₁₉	—	8	4	no	—
254	C₂²×C₁₉	—	8	8	no	—
255	C₂²×C₁₉	—	8	32	no	—
256	C₂²×C₁₉	—	8	1	no	—
257	C₂²×C₁₉	—	8	1	no	—
258	C₂²×C₁₉	—	8	1	no	—
259	C₂²×C₁₉	#453	1	2	yes	complemented
260	C₂²×C₁₉	C₂×#120	1	2	yes	—
261	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
262	C₄×C₁₉	—	2	8	no	—
263	C₄×C₁₉	—	2	2	no	—
264	C₄×C₁₉	—	4	4	no	—
265	C₄×C₁₉	—	8	1	no	—
266	C₄×C₁₉	C₂×#120	1	4	yes	—
267	C₂×H(5,𝔽₂)	—	2	16	no	—
268	C₂×H(5,𝔽₂)	—	2	4	no	—
269	C₂×H(5,𝔽₂)	—	2	2	no	—
270	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	4	yes	—
271	C₂²×#41	—	2	2	no	—
272	C₂²×#41	C₂²×C₁₉	1	2	yes	—
273	C₂³×D₄	—	2	2	no	—
274	C₂³×D₄	—	2	2	no	—
275	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	complemented
277	C₂×#127	C₂²×C₁₉	1	2	yes	complemented
278	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
279	C₂×#120	—	2	2	no	—
280	#453	—	2	16	no	—
281	#449	—	2	4	no	—
282	#448	—	2	2	no	—
283	#447	—	2	2	no	—
284	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
285	#417	C₂²×C₁₉	1	4	yes	complemented
286	C₂×#100	C₂²×C₁₉	1	4	yes	complemented
287	#407	C₂²×C₁₉	1	2	yes	complemented
288	#392	—	2	2	no	—
289	#390	C₂²×C₁₉	1	2	yes	complemented
290	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
291	C₂×C₁₉	—	2	2	no	—
292	C₂×C₁₉	—	2	2	no	—
293	C₂×C₁₉	—	4	1	no	—
294	C₂×C₁₉	—	4	8	no	—
295	C₂×C₁₉	—	4	8	no	—
296	C₂×C₁₉	—	16	1	no	—
297	C₂×C₁₉	#2846	1	1	yes	characteristic
298	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
299	C₂×C₁₉	#3019	1	1	yes	characteristic
300	C₂⁵	—	2	2	no	—
301	C₂⁵	D₄×C₁₉	1	2	yes	—
302	H(5,𝔽₂)	—	2	32	no	—
303	H(5,𝔽₂)	—	2	32	no	—
304	H(5,𝔽₂)	—	2	32	no	—
305	H(5,𝔽₂)	—	2	16	no	—
306	H(5,𝔽₂)	—	2	8	no	—
307	H(5,𝔽₂)	D₄×C₁₉	1	16	yes	complemented
308	C₂×#41	—	2	32	no	—
309	C₂×#41	—	2	8	no	—
310	C₂×#41	—	2	16	no	—
311	C₂×#41	—	2	8	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	2	2	no	—
314	C₂×#41	D₄×C₁₉	1	4	yes	complemented
315	C₂×#41	C₂³×C₁₉	1	4	yes	—
316	C₂²×Q₈	D₄×C₁₉	1	2	yes	complemented
317	C₂²×D₄	—	2	4	no	—
318	C₂²×D₄	—	2	32	no	—
319	C₂²×D₄	—	2	32	no	—
320	C₂²×D₄	—	2	8	no	—
321	C₂²×D₄	—	2	8	no	—
322	C₂²×D₄	—	2	2	no	—
323	C₂²×D₄	—	2	8	no	—
324	C₂²×D₄	—	2	8	no	—
325	C₂²×D₄	—	2	8	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	D₄×C₁₉	1	2	yes	—
331	C₂²×D₄	D₄×C₁₉	1	2	yes	complemented
332	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
333	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic, complemented
334	C₂³×C₄	—	2	2	no	—
335	C₂³×C₄	—	2	2	no	—
336	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
337	AGL(1,ℤ/8)	—	2	16	no	—
338	C₂×SD₁₆	—	2	4	no	—
339	C₂×D₈	—	2	4	no	—
340	C₂×M₁₆	C₂³×C₁₉	1	4	yes	complemented
341	#127	—	2	8	no	—
342	#121	—	2	2	no	—
343	#121	—	2	2	no	—
344	#120	—	4	8	no	—
345	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic, complemented
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	4	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₄²	C₂³×C₁₉	1	2	yes	complemented
350	#104	—	2	16	no	—
351	#103	—	2	4	no	—
352	#102	—	2	4	no	—
353	#100	—	2	8	no	—
354	C₂²⋊C₈	—	2	2	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	#95	—	2	1	no	—
357	C₁₉	#32888	1	1	yes	characteristic, direct product factor, Sylow
358	C₂⁴	—	2	16	no	—
359	C₂⁴	—	2	8	no	—
360	C₂⁴	—	2	2	no	—
361	C₂⁴	—	2	2	no	—
362	C₂⁴	—	2	8	no	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	—	2	1	no	—
365	C₂⁴	—	4	4	no	—
366	C₂⁴	—	8	2	no	—
367	C₂⁴	—	8	4	no	—
368	C₂⁴	—	8	4	no	—
369	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
371	#41	—	2	64	no	—
372	#41	—	2	16	no	—
373	#41	—	2	32	no	—
374	#41	—	2	16	no	—
375	#41	—	2	32	no	—
376	#41	—	2	8	no	—
377	#41	—	2	8	no	—
378	#41	—	2	8	no	—
379	#41	C₂×D₄×C₁₉	1	16	yes	—
380	C₂×Q₈	—	2	8	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
383	C₂×D₄	—	2	32	no	—
384	C₂×D₄	—	2	16	no	—
385	C₂×D₄	—	2	16	no	—
386	C₂×D₄	—	2	16	no	—
387	C₂×D₄	—	2	64	no	—
388	C₂×D₄	—	2	64	no	—
389	C₂×D₄	—	2	32	no	—
390	C₂×D₄	—	2	32	no	—
391	C₂×D₄	—	2	16	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	32	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	32	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	4	8	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	8	no	—
409	C₂×D₄	—	8	4	no	—
410	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
411	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
412	C₂²×C₄	—	2	16	no	—
413	C₂²×C₄	—	2	16	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
425	SD₁₆	—	4	8	no	—
426	D₈	—	4	8	no	—
427	M₁₆	—	2	8	no	—
428	C₂×C₈	—	2	4	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	4	8	no	—
432	C₂²⋊C₄	—	4	2	no	—
433	C₄²	—	2	4	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	8	no	—
437	C₂³	—	2	32	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	4	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	16	no	—
457	C₂³	—	8	32	no	—
458	C₂³	—	8	8	no	—
459	C₂³	—	8	8	no	—
460	C₂³	C₁₉×#120	1	1	yes	characteristic
461	C₂³	C₁₉×#120	1	1	yes	characteristic
462	C₂³	C₁₉×#120	1	8	yes	—
463	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
464	Q₈	—	2	8	no	—
465	Q₈	—	2	4	no	—
466	Q₈	C₁₉×#120	1	8	yes	complemented
467	D₄	—	2	64	no	—
468	D₄	—	2	16	no	—
469	D₄	—	2	16	no	—
470	D₄	—	2	8	no	—
471	D₄	—	2	16	no	—
472	D₄	—	2	16	no	—
473	D₄	—	2	4	no	—
474	D₄	—	4	4	no	—
475	D₄	—	8	16	no	—
476	D₄	—	8	2	no	—
477	D₄	—	8	2	no	—
478	D₄	C₁₉×#120	1	8	yes	complemented
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	32	no	—
481	C₂×C₄	—	2	16	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	16	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	C₁₉×#120	1	2	yes	—
493	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
494	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
495	C₈	—	4	4	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	8	no	—
504	C₂²	—	2	8	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	8	no	—
507	C₂²	—	4	16	no	—
508	C₂²	—	4	16	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	8	4	no	—
514	C₂²	—	8	4	no	—
515	C₂²	—	8	8	no	—
516	C₂²	—	8	32	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	8	1	no	—
519	C₂²	—	8	1	no	—
520	C₂²	C₁₉×#453	1	2	yes	complemented
521	C₂²	C₂×C₁₉×#120	1	2	yes	—
522	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
523	C₄	—	2	8	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	8	1	no	—
527	C₄	C₂×C₁₉×#120	1	4	yes	—
528	C₂	—	2	2	no	—
529	C₂	—	2	2	no	—
530	C₂	—	4	1	no	—
531	C₂	—	4	8	no	—
532	C₂	—	4	8	no	—
533	C₂	—	16	1	no	—
534	C₂	C₁₉×#2846	1	1	yes	characteristic
535	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
536	C₂	C₁₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₁₉×#453	C₂	semidirect
3. C₁₉×#3006	C₂	semidirect
4. C₁₉×#2433	C₂	semidirect
5. C₁₉×#1792	C₂	semidirect
6. C₁₉×#1789	C₂	semidirect
7. C₁₉×#1783	C₂	semidirect
17. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂×C₁₉×#127	C₂²	semidirect
19. C₂×C₁₉×#121	C₂²	semidirect
25. C₂×C₁₉×#104	C₂²	semidirect
26. C₁₉×#417	C₂²	semidirect
27. C₂×C₁₉×#100	C₂²	semidirect
28. C₁₉×#407	C₂²	semidirect
30. C₁₉×#390	C₂²	semidirect
31. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
39. C₁₉×H(5,𝔽₂)	D₄	semidirect
46. C₂×#41×C₁₉	D₄	semidirect
48. C₂²×Q₈×C₁₉	D₄	semidirect
63. C₂²×D₄×C₁₉	D₄	semidirect
65. C₂²×D₄×C₁₉	C₂³	semidirect
72. C₂×M₁₆×C₁₉	C₂³	semidirect
77. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
81. C₂×C₄²×C₁₉	C₂³	semidirect
165. #32888	C₁₉	direct (N × H)
198. Q₈×C₁₉	#120	semidirect
210. D₄×C₁₉	#120	semidirect
228. C₂²×H(5,𝔽₂)	C₂×C₁₉	semidirect
229. C₂×#453	C₂×C₁₉	semidirect
230. #3006	C₂×C₁₉	semidirect
231. #2433	C₂×C₁₉	semidirect
232. #1792	C₂×C₁₉	semidirect
233. #1789	C₂×C₁₉	semidirect
234. #1783	C₂×C₁₉	semidirect
259. C₂²×C₁₉	#453	semidirect
276. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
277. C₂×#127	C₂²×C₁₉	semidirect
278. C₂×#121	C₂²×C₁₉	semidirect
284. C₂×#104	C₂²×C₁₉	semidirect
285. #417	C₂²×C₁₉	semidirect
286. C₂×#100	C₂²×C₁₉	semidirect
287. #407	C₂²×C₁₉	semidirect
289. #390	C₂²×C₁₉	semidirect
290. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
307. H(5,𝔽₂)	D₄×C₁₉	semidirect
314. C₂×#41	D₄×C₁₉	semidirect
316. C₂²×Q₈	D₄×C₁₉	semidirect
331. C₂²×D₄	D₄×C₁₉	semidirect
333. C₂²×D₄	C₂³×C₁₉	semidirect
340. C₂×M₁₆	C₂³×C₁₉	semidirect
345. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
349. C₂×C₄²	C₂³×C₁₉	semidirect
357. C₁₉	#32888	direct (N × H)
466. Q₈	C₁₉×#120	semidirect
478. D₄	C₁₉×#120	semidirect
520. C₂²	C₁₉×#453	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×H(5,𝔽₂)	2
C₂×C₁₉×#453	2
C₁₉×#3006	2
C₁₉×#2433	2
C₁₉×#1792	2
C₁₉×#1789	2
C₁₉×#1783	2
#32888	19

Subgroups — C19×#32888 #18038847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32888 #18038847