Subgroups — C₁₉×#18350 #18024309

Order 4864.

1276 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3192	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2635	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1616	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1613	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1598	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1595	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1510	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×H(5,𝔽₂)	—	2	1	no	—
11	C₁₉×#547	—	2	2	no	—
12	C₁₉×#546	—	2	4	no	—
13	D₄²×C₁₉	—	2	2	no	—
14	C₁₉×#537	C₂²	1	2	yes	—
15	C₁₉×#534	—	2	1	no	—
16	C₁₉×#534	C₂²	1	2	yes	—
17	C₁₉×#532	—	2	1	no	—
18	C₂×C₁₉×#121	—	2	1	no	—
19	C₂×C₁₉×#121	C₂²	1	2	yes	—
20	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#481	—	2	2	no	—
23	C₁₉×#481	C₂²	1	4	yes	complemented
24	C₁₉×#469	—	2	4	no	—
25	C₁₉×#447	—	2	2	no	—
26	C₁₉×#447	C₂²	1	4	yes	complemented
27	C₁₉×#407	C₂²	1	2	yes	complemented
28	C₁₉×#400	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#399	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#394	—	2	1	no	—
31	C₁₉×#394	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#392	—	2	1	no	—
33	C₁₉×#392	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#388	—	2	1	no	—
35	C₁₉×#386	—	2	1	no	—
36	C₁₉×#381	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#327	C₂²	1	4	yes	complemented
38	C₁₉×#327	C₂²	1	4	yes	complemented
39	C₁₉×#324	C₂²	1	2	yes	complemented
40	C₁₉×#323	C₂²	1	2	yes	complemented
41	C₁₉×H(5,𝔽₂)	—	4	4	no	—
42	C₁₉×H(5,𝔽₂)	—	4	4	no	—
43	C₂×#41×C₁₉	—	2	4	no	—
44	C₂×#41×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	2	no	—
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	D₄	1	2	yes	complemented
53	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×D₈×C₁₉	—	2	4	no	—
57	C₂×M₁₆×C₁₉	—	2	2	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×#127	—	2	1	no	—
60	C₁₉×#124	—	2	2	no	—
61	C₁₉×#123	—	2	4	no	—
62	C₁₉×#123	—	2	4	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×#121	—	2	2	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	—	2	4	no	—
67	C₁₉×#121	—	2	2	no	—
68	C₁₉×#121	—	2	2	no	—
69	C₁₉×#121	—	2	2	no	—
70	C₁₉×#121	—	2	2	no	—
71	C₁₉×#121	—	2	2	no	—
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	D₄	1	4	yes	complemented
74	C₁₉×#121	C₂³	1	4	yes	—
75	C₁₉×#120	—	2	4	no	—
76	C₁₉×#120	—	2	4	no	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₄×D₄×C₁₉	—	2	2	no	—
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	complemented
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
97	C₁₉×#106	—	2	4	no	—
98	C₁₉×#102	—	2	4	no	—
99	C₁₉×#102	—	2	4	no	—
100	C₁₉×C₂²⋊C₈	—	2	2	no	—
101	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	—	2	1	no	—
104	C₁₉×#95	—	2	1	no	—
105	C₁₉×#95	C₂³	1	1	yes	characteristic
106	C₁₉×#95	C₂³	1	1	yes	characteristic
107	C₂⁴×C₁₉	—	2	2	no	—
108	C₂⁴×C₁₉	—	2	2	no	—
109	C₂⁴×C₁₉	—	2	1	no	—
110	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
112	#41×C₁₉	—	4	4	no	—
113	#41×C₁₉	—	4	16	no	—
114	#41×C₁₉	—	4	4	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	4	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	4	no	—
121	C₂×D₄×C₁₉	—	2	4	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	4	16	no	—
128	C₂×D₄×C₁₉	—	4	4	no	—
129	C₂×D₄×C₁₉	—	4	4	no	—
130	C₂×D₄×C₁₉	—	4	4	no	—
131	C₂×D₄×C₁₉	—	4	4	no	—
132	C₂×D₄×C₁₉	—	4	2	no	—
133	C₂×D₄×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	8	1	no	—
135	C₂×D₄×C₁₉	—	8	2	no	—
136	C₂×D₄×C₁₉	—	8	2	no	—
137	C₂×D₄×C₁₉	—	8	1	no	—
138	C₂×D₄×C₁₉	—	8	1	no	—
139	C₂×D₄×C₁₉	—	8	1	no	—
140	C₂×D₄×C₁₉	—	8	1	no	—
141	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	4	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	8	1	no	—
151	C₂²×C₄×C₁₉	—	8	1	no	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
159	D₈×C₁₉	—	8	4	no	—
160	M₁₆×C₁₉	—	8	2	no	—
161	C₂×C₈×C₁₉	—	2	4	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	8	1	no	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	4	1	no	—
176	C₂²⋊C₄×C₁₉	—	4	1	no	—
177	C₂²⋊C₄×C₁₉	—	4	2	no	—
178	C₂²⋊C₄×C₁₉	—	8	1	no	—
179	C₂²⋊C₄×C₁₉	—	8	1	no	—
180	C₂²⋊C₄×C₁₉	—	8	1	no	—
181	C₂²⋊C₄×C₁₉	—	8	1	no	—
182	C₄²×C₁₉	—	2	1	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	#18350	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₁₉	—	2	1	no	—
186	C₂³×C₁₉	—	2	1	no	—
187	C₂³×C₁₉	—	2	1	no	—
188	C₂³×C₁₉	—	2	1	no	—
189	C₂³×C₁₉	—	2	4	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	—	4	1	no	—
192	C₂³×C₁₉	—	4	1	no	—
193	C₂³×C₁₉	—	4	1	no	—
194	C₂³×C₁₉	—	4	4	no	—
195	C₂³×C₁₉	—	4	4	no	—
196	C₂³×C₁₉	—	4	1	no	—
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	—	4	1	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	—	8	2	no	—
204	C₂³×C₁₉	—	8	2	no	—
205	C₂³×C₁₉	—	8	2	no	—
206	C₂³×C₁₉	—	8	2	no	—
207	C₂³×C₁₉	#120	1	2	yes	—
208	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
209	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
210	Q₈×C₁₉	—	4	4	no	—
211	D₄×C₁₉	—	2	8	no	—
212	D₄×C₁₉	—	4	4	no	—
213	D₄×C₁₉	—	4	4	no	—
214	D₄×C₁₉	—	4	4	no	—
215	D₄×C₁₉	—	4	4	no	—
216	D₄×C₁₉	—	4	8	no	—
217	D₄×C₁₉	—	4	8	no	—
218	D₄×C₁₉	—	4	4	no	—
219	D₄×C₁₉	—	4	4	no	—
220	D₄×C₁₉	—	8	2	no	—
221	D₄×C₁₉	—	8	2	no	—
222	D₄×C₁₉	—	8	4	no	—
223	D₄×C₁₉	—	8	4	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	4	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	8	no	—
235	C₂×C₄×C₁₉	—	4	4	no	—
236	C₂×C₄×C₁₉	—	4	4	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	8	1	no	—
249	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
252	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
253	C₈×C₁₉	—	4	4	no	—
254	#3496	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#3192	C₂×C₁₉	1	2	yes	complemented
256	#2635	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1616	C₂×C₁₉	1	2	yes	complemented
258	#1613	C₂×C₁₉	1	2	yes	complemented
259	#1598	C₂×C₁₉	1	2	yes	complemented
260	#1595	C₂×C₁₉	1	2	yes	complemented
261	#1510	C₂×C₁₉	1	2	yes	complemented
262	#1465	C₂×C₁₉	1	1	yes	characteristic, complemented
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	2	2	no	—
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	2	no	—
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	4	no	—
273	C₂²×C₁₉	—	4	4	no	—
274	C₂²×C₁₉	—	4	4	no	—
275	C₂²×C₁₉	—	8	1	no	—
276	C₂²×C₁₉	—	8	1	no	—
277	C₂²×C₁₉	—	8	1	no	—
278	C₂²×C₁₉	—	8	1	no	—
279	C₂²×C₁₉	—	8	1	no	—
280	C₂²×C₁₉	—	8	1	no	—
281	C₂²×C₁₉	—	8	1	no	—
282	C₂²×C₁₉	—	8	1	no	—
283	C₂²×C₁₉	—	8	1	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	16	4	no	—
286	C₂²×C₁₉	—	16	4	no	—
287	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
288	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
289	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₄×C₁₉	—	2	2	no	—
291	C₄×C₁₉	—	2	2	no	—
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	4	4	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	4	1	no	—
297	C₄×C₁₉	—	8	1	no	—
298	C₄×C₁₉	—	8	1	no	—
299	C₄×C₁₉	—	8	1	no	—
300	C₂×H(5,𝔽₂)	—	2	1	no	—
301	#547	—	2	2	no	—
302	#546	—	2	4	no	—
303	D₄²	—	2	2	no	—
304	#537	C₂²×C₁₉	1	2	yes	—
305	#534	—	2	1	no	—
306	#534	C₂²×C₁₉	1	2	yes	—
307	#532	—	2	1	no	—
308	C₂×#121	—	2	1	no	—
309	C₂×#121	C₂²×C₁₉	1	2	yes	—
310	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
311	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
312	#481	—	2	2	no	—
313	#481	C₂²×C₁₉	1	4	yes	complemented
314	#469	—	2	4	no	—
315	#447	—	2	2	no	—
316	#447	C₂²×C₁₉	1	4	yes	complemented
317	#407	C₂²×C₁₉	1	2	yes	complemented
318	#400	C₂²×C₁₉	1	1	yes	characteristic, complemented
319	#399	C₂²×C₁₉	1	1	yes	characteristic, complemented
320	#394	—	2	1	no	—
321	#394	C₂²×C₁₉	1	1	yes	characteristic, complemented
322	#392	—	2	1	no	—
323	#392	C₂²×C₁₉	1	1	yes	characteristic, complemented
324	#388	—	2	1	no	—
325	#386	—	2	1	no	—
326	#381	C₂²×C₁₉	1	1	yes	characteristic, complemented
327	#327	C₂²×C₁₉	1	4	yes	complemented
328	#327	C₂²×C₁₉	1	4	yes	complemented
329	#324	C₂²×C₁₉	1	2	yes	complemented
330	#323	C₂²×C₁₉	1	2	yes	complemented
331	C₂×C₁₉	—	2	1	no	—
332	C₂×C₁₉	—	2	1	no	—
333	C₂×C₁₉	—	4	2	no	—
334	C₂×C₁₉	—	4	2	no	—
335	C₂×C₁₉	—	8	4	no	—
336	C₂×C₁₉	—	16	1	no	—
337	C₂×C₁₉	#3003	1	1	yes	characteristic
338	C₂×C₁₉	#3021	1	1	yes	characteristic
339	C₂×C₁₉	#3026	1	1	yes	characteristic
340	H(5,𝔽₂)	—	4	4	no	—
341	H(5,𝔽₂)	—	4	4	no	—
342	C₂×#41	—	2	4	no	—
343	C₂×#41	—	2	2	no	—
344	C₂²×D₄	—	2	4	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
351	C₂²×D₄	D₄×C₁₉	1	2	yes	complemented
352	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
353	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×D₈	—	2	4	no	—
356	C₂×M₁₆	—	2	2	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	#127	—	2	1	no	—
359	#124	—	2	2	no	—
360	#123	—	2	4	no	—
361	#123	—	2	4	no	—
362	C₂²⋊Q₈	—	2	4	no	—
363	#121	—	2	2	no	—
364	#121	—	2	2	no	—
365	#121	—	2	4	no	—
366	#121	—	2	2	no	—
367	#121	—	2	2	no	—
368	#121	—	2	2	no	—
369	#121	—	2	2	no	—
370	#121	—	2	2	no	—
371	#121	—	2	2	no	—
372	#121	D₄×C₁₉	1	4	yes	complemented
373	#121	C₂³×C₁₉	1	4	yes	—
374	#120	—	2	4	no	—
375	#120	—	2	4	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	complemented
383	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
395	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
396	#106	—	2	4	no	—
397	#102	—	2	4	no	—
398	#102	—	2	4	no	—
399	C₂²⋊C₈	—	2	2	no	—
400	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	C₂³×C₁₉	1	1	yes	characteristic
405	#95	C₂³×C₁₉	1	1	yes	characteristic
406	C₁₉	#18350	1	1	yes	characteristic, direct product factor, Sylow
407	C₂⁴	—	2	2	no	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	2	1	no	—
410	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
412	#41	—	4	4	no	—
413	#41	—	4	16	no	—
414	#41	—	4	4	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	4	16	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	—	4	2	no	—
434	C₂×D₄	—	8	1	no	—
435	C₂×D₄	—	8	2	no	—
436	C₂×D₄	—	8	2	no	—
437	C₂×D₄	—	8	1	no	—
438	C₂×D₄	—	8	1	no	—
439	C₂×D₄	—	8	1	no	—
440	C₂×D₄	—	8	1	no	—
441	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	8	1	no	—
451	C₂²×C₄	—	8	1	no	—
452	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
457	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
459	D₈	—	8	4	no	—
460	M₁₆	—	8	2	no	—
461	C₂×C₈	—	2	4	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	8	1	no	—
468	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	8	1	no	—
479	C₂²⋊C₄	—	8	1	no	—
480	C₂²⋊C₄	—	8	1	no	—
481	C₂²⋊C₄	—	8	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	8	2	no	—
503	C₂³	—	8	2	no	—
504	C₂³	—	8	2	no	—
505	C₂³	—	8	2	no	—
506	C₂³	C₁₉×#120	1	2	yes	—
507	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
508	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
509	Q₈	—	4	4	no	—
510	D₄	—	2	8	no	—
511	D₄	—	4	4	no	—
512	D₄	—	4	4	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	4	no	—
515	D₄	—	4	8	no	—
516	D₄	—	4	8	no	—
517	D₄	—	4	4	no	—
518	D₄	—	4	4	no	—
519	D₄	—	8	2	no	—
520	D₄	—	8	2	no	—
521	D₄	—	8	4	no	—
522	D₄	—	8	4	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	8	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	8	1	no	—
548	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
549	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
550	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
552	C₈	—	4	4	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	1	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	16	4	no	—
576	C₂²	—	16	4	no	—
577	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
578	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
579	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	4	4	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	1	no	—
592	C₂	—	4	2	no	—
593	C₂	—	4	2	no	—
594	C₂	—	8	4	no	—
595	C₂	—	16	1	no	—
596	C₂	C₁₉×#3003	1	1	yes	characteristic
597	C₂	C₁₉×#3021	1	1	yes	characteristic
598	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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. C₁₉×#3496	C₂	semidirect
2. C₁₉×#3192	C₂	semidirect
3. C₁₉×#2635	C₂	semidirect
4. C₁₉×#1616	C₂	semidirect
5. C₁₉×#1613	C₂	semidirect
6. C₁₉×#1598	C₂	semidirect
7. C₁₉×#1595	C₂	semidirect
8. C₁₉×#1510	C₂	semidirect
9. C₁₉×#1465	C₂	semidirect
20. C₂×C₁₉×#121	C₂²	semidirect
23. C₁₉×#481	C₂²	semidirect
26. C₁₉×#447	C₂²	semidirect
27. C₁₉×#407	C₂²	semidirect
28. C₁₉×#400	C₂²	semidirect
29. C₁₉×#399	C₂²	semidirect
31. C₁₉×#394	C₂²	semidirect
33. C₁₉×#392	C₂²	semidirect
36. C₁₉×#381	C₂²	semidirect
37. C₁₉×#327	C₂²	semidirect
38. C₁₉×#327	C₂²	semidirect
39. C₁₉×#324	C₂²	semidirect
40. C₁₉×#323	C₂²	semidirect
52. C₂²×D₄×C₁₉	D₄	semidirect
73. C₁₉×#121	D₄	semidirect
83. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
184. #18350	C₁₉	direct (N × H)
254. #3496	C₂×C₁₉	semidirect
255. #3192	C₂×C₁₉	semidirect
256. #2635	C₂×C₁₉	semidirect
257. #1616	C₂×C₁₉	semidirect
258. #1613	C₂×C₁₉	semidirect
259. #1598	C₂×C₁₉	semidirect
260. #1595	C₂×C₁₉	semidirect
261. #1510	C₂×C₁₉	semidirect
262. #1465	C₂×C₁₉	semidirect
310. C₂×#121	C₂²×C₁₉	semidirect
313. #481	C₂²×C₁₉	semidirect
316. #447	C₂²×C₁₉	semidirect
317. #407	C₂²×C₁₉	semidirect
318. #400	C₂²×C₁₉	semidirect
319. #399	C₂²×C₁₉	semidirect
321. #394	C₂²×C₁₉	semidirect
323. #392	C₂²×C₁₉	semidirect
326. #381	C₂²×C₁₉	semidirect
327. #327	C₂²×C₁₉	semidirect
328. #327	C₂²×C₁₉	semidirect
329. #324	C₂²×C₁₉	semidirect
330. #323	C₂²×C₁₉	semidirect
351. C₂²×D₄	D₄×C₁₉	semidirect
372. #121	D₄×C₁₉	semidirect
382. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
406. C₁₉	#18350	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3496	2
C₁₉×#3192	2
C₁₉×#2635	2
C₁₉×#1616	2
C₁₉×#1613	2
C₁₉×#1598	2
C₁₉×#1595	2
C₁₉×#1510	2
C₁₉×#1465	2
#18350	19

Subgroups — C19×#18350 #18024309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18350 #18024309