Subgroups — C₁₉×#32920 #18038879

Order 4864.

1590 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3038	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#453	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2541	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1887	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1883	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1806	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1800	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)	C₂²	1	4	yes	—
11	C₂×C₁₉×#127	C₂²	1	2	yes	—
12	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₁₉×#121	—	2	2	no	—
14	C₁₉×#520	—	2	2	no	—
15	C₁₉×#520	C₂²	1	2	yes	—
16	C₁₉×#518	—	2	2	no	—
17	C₁₉×#518	—	2	2	no	—
18	C₁₉×#518	C₂²	1	1	yes	characteristic
19	C₄×#41×C₁₉	—	2	2	no	—
20	C₄×#41×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₉	—	2	2	no	—
22	C₂×C₄×D₄×C₁₉	—	2	2	no	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#460	—	2	2	no	—
25	C₁₉×#460	—	2	2	no	—
26	C₁₉×#459	—	2	2	no	—
27	C₁₉×#459	—	2	2	no	—
28	C₁₉×#453	—	2	8	no	—
29	C₁₉×#423	C₂²	1	2	yes	complemented
30	C₂×C₁₉×#104	C₂²	1	4	yes	—
31	C₁₉×#418	C₂²	1	4	yes	complemented
32	C₂×C₁₉×#100	C₂²	1	2	yes	—
33	C₁₉×#392	—	2	2	no	—
34	C₁₉×#390	C₂²	1	2	yes	complemented
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#343	C₂²	1	2	yes	complemented
37	C₁₉×#339	C₂²	1	4	yes	complemented
38	C₁₉×H(5,𝔽₂)	—	2	4	no	—
39	C₁₉×H(5,𝔽₂)	—	2	2	no	—
40	C₁₉×H(5,𝔽₂)	D₄	1	4	yes	complemented
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	—	2	2	no	—
51	C₂³×C₄×C₁₉	D₄	1	2	yes	—
52	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
53	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
54	C₂×SD₁₆×C₁₉	—	2	4	no	—
55	C₂×D₈×C₁₉	—	2	4	no	—
56	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
57	C₁₉×#127	—	2	4	no	—
58	C₁₉×#127	—	2	4	no	—
59	C₁₉×#127	—	2	2	no	—
60	C₁₉×#127	—	2	2	no	—
61	C₁₉×#121	—	4	8	no	—
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
64	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
65	C₄×D₄×C₁₉	—	2	4	no	—
66	C₄×D₄×C₁₉	—	2	4	no	—
67	C₄×D₄×C₁₉	—	2	4	no	—
68	C₄×D₄×C₁₉	—	2	4	no	—
69	C₄×D₄×C₁₉	—	2	2	no	—
70	C₄×D₄×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	—	2	4	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	2	2	no	—
76	C₄×D₄×C₁₉	—	2	2	no	—
77	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
78	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
79	C₁₉×#117	—	2	4	no	—
80	C₁₉×#117	—	2	2	no	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
92	C₂×C₄²×C₁₉	—	2	2	no	—
93	C₂×C₄²×C₁₉	—	2	2	no	—
94	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×C₄⋊C₈	—	2	2	no	—
97	C₁₉×C₄⋊C₈	—	2	2	no	—
98	C₁₉×#104	—	2	8	no	—
99	C₁₉×#102	—	2	4	no	—
100	C₁₉×#102	—	2	4	no	—
101	C₁₉×#100	—	2	4	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₂⁴×C₁₉	—	2	2	no	—
104	C₂⁴×C₁₉	—	2	2	no	—
105	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
106	#41×C₁₉	—	2	8	no	—
107	#41×C₁₉	—	2	8	no	—
108	#41×C₁₉	—	2	2	no	—
109	#41×C₁₉	—	2	2	no	—
110	#41×C₁₉	C₂×D₄	1	4	yes	—
111	#41×C₁₉	#41	1	4	yes	—
112	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	2	8	no	—
115	C₂×D₄×C₁₉	—	2	8	no	—
116	C₂×D₄×C₁₉	—	2	8	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	8	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	4	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	4	no	—
125	C₂×D₄×C₁₉	—	4	4	no	—
126	C₂×D₄×C₁₉	—	4	8	no	—
127	C₂×D₄×C₁₉	—	4	8	no	—
128	C₂×D₄×C₁₉	—	4	2	no	—
129	C₂×D₄×C₁₉	—	4	1	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	—	8	2	no	—
132	C₂×D₄×C₁₉	—	8	4	no	—
133	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₁₉	#41	1	2	yes	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	4	4	no	—
147	C₂²×C₄×C₁₉	—	8	4	no	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
152	SD₁₆×C₁₉	—	4	8	no	—
153	D₈×C₁₉	—	4	8	no	—
154	M₁₆×C₁₉	—	2	4	no	—
155	M₁₆×C₁₉	—	2	4	no	—
156	C₂×C₈×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₁₉	—	2	4	no	—
165	C₂²⋊C₄×C₁₉	—	2	4	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	4	8	no	—
171	C₄²×C₁₉	—	2	4	no	—
172	C₄²×C₁₉	—	2	2	no	—
173	C₄²×C₁₉	—	2	2	no	—
174	C₄²×C₁₉	—	2	2	no	—
175	C₄²×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	—	2	2	no	—
177	C₄²×C₁₉	C₂×D₄	1	2	yes	—
178	C₄²×C₁₉	C₂×D₄	1	2	yes	—
179	#32920	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂³×C₁₉	—	2	8	no	—
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	—	4	2	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	4	no	—
187	C₂³×C₁₉	—	4	4	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	8	2	no	—
192	C₂³×C₁₉	—	8	2	no	—
193	C₂³×C₁₉	#121	1	4	yes	—
194	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₁₉	—	2	2	no	—
196	Q₈×C₁₉	#121	1	4	yes	complemented
197	D₄×C₁₉	—	2	16	no	—
198	D₄×C₁₉	—	2	4	no	—
199	D₄×C₁₉	—	2	4	no	—
200	D₄×C₁₉	—	2	4	no	—
201	D₄×C₁₉	—	2	2	no	—
202	D₄×C₁₉	—	2	4	no	—
203	D₄×C₁₉	—	4	4	no	—
204	D₄×C₁₉	—	4	4	no	—
205	D₄×C₁₉	—	8	2	no	—
206	D₄×C₁₉	—	8	4	no	—
207	D₄×C₁₉	—	8	16	no	—
208	D₄×C₁₉	—	8	2	no	—
209	D₄×C₁₉	#121	1	4	yes	complemented
210	C₂×C₄×C₁₉	—	2	8	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	4	no	—
223	C₂×C₄×C₁₉	—	4	4	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	8	2	no	—
226	C₂×C₄×C₁₉	—	8	2	no	—
227	C₂×C₄×C₁₉	—	8	2	no	—
228	C₂×C₄×C₁₉	—	8	4	no	—
229	C₂×C₄×C₁₉	—	8	2	no	—
230	C₂×C₄×C₁₉	#120	1	2	yes	—
231	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
236	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
237	C₈×C₁₉	—	4	4	no	—
238	C₄×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#3038	C₂×C₁₉	1	2	yes	complemented
240	C₂×#453	C₂×C₁₉	1	2	yes	complemented
241	#2541	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#1887	C₂×C₁₉	1	2	yes	complemented
243	#1883	C₂×C₁₉	1	4	yes	complemented
244	#1806	C₂×C₁₉	1	2	yes	complemented
245	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	4	no	—
249	C₂²×C₁₉	—	2	4	no	—
250	C₂²×C₁₉	—	4	4	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	8	2	no	—
256	C₂²×C₁₉	—	8	4	no	—
257	C₂²×C₁₉	—	8	4	no	—
258	C₂²×C₁₉	—	8	8	no	—
259	C₂²×C₁₉	—	8	2	no	—
260	C₂²×C₁₉	—	8	2	no	—
261	C₂²×C₁₉	—	8	2	no	—
262	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
263	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
264	C₂²×C₁₉	#525	1	1	yes	characteristic
265	C₄×C₁₉	—	2	4	no	—
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	2	2	no	—
268	C₄×C₁₉	—	4	4	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	#453	1	2	yes	complemented
273	C₄×C₁₉	C₂×#121	1	2	yes	—
274	C₄×C₁₉	#525	1	2	yes	—
275	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	—
277	C₂×#127	C₂²×C₁₉	1	2	yes	—
278	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
279	C₂×#121	—	2	2	no	—
280	#520	—	2	2	no	—
281	#520	C₂²×C₁₉	1	2	yes	—
282	#518	—	2	2	no	—
283	#518	—	2	2	no	—
284	#518	C₂²×C₁₉	1	1	yes	characteristic
285	C₄×#41	—	2	2	no	—
286	C₄×#41	C₂²×C₁₉	1	2	yes	—
287	C₂×C₄×D₄	—	2	2	no	—
288	C₂×C₄×D₄	—	2	2	no	—
289	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
290	#460	—	2	2	no	—
291	#460	—	2	2	no	—
292	#459	—	2	2	no	—
293	#459	—	2	2	no	—
294	#453	—	2	8	no	—
295	#423	C₂²×C₁₉	1	2	yes	complemented
296	C₂×#104	C₂²×C₁₉	1	4	yes	—
297	#418	C₂²×C₁₉	1	4	yes	complemented
298	C₂×#100	C₂²×C₁₉	1	2	yes	—
299	#392	—	2	2	no	—
300	#390	C₂²×C₁₉	1	2	yes	complemented
301	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
302	#343	C₂²×C₁₉	1	2	yes	complemented
303	#339	C₂²×C₁₉	1	4	yes	complemented
304	C₂×C₁₉	—	2	1	no	—
305	C₂×C₁₉	—	2	1	no	—
306	C₂×C₁₉	—	4	4	no	—
307	C₂×C₁₉	—	4	4	no	—
308	C₂×C₁₉	—	16	2	no	—
309	C₂×C₁₉	#2847	1	1	yes	characteristic
310	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
311	C₂×C₁₉	#3021	1	1	yes	characteristic
312	H(5,𝔽₂)	—	2	4	no	—
313	H(5,𝔽₂)	—	2	2	no	—
314	H(5,𝔽₂)	D₄×C₁₉	1	4	yes	complemented
315	C₂×#41	—	2	2	no	—
316	C₂×#41	C₂³×C₁₉	1	2	yes	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	4	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
323	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
324	C₂³×C₄	—	2	2	no	—
325	C₂³×C₄	D₄×C₁₉	1	2	yes	—
326	AGL(1,ℤ/8)	—	2	8	no	—
327	AGL(1,ℤ/8)	—	2	8	no	—
328	C₂×SD₁₆	—	2	4	no	—
329	C₂×D₈	—	2	4	no	—
330	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
331	#127	—	2	4	no	—
332	#127	—	2	4	no	—
333	#127	—	2	2	no	—
334	#127	—	2	2	no	—
335	#121	—	4	8	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
338	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
339	C₄×D₄	—	2	4	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	4	no	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
352	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
353	#117	—	2	4	no	—
354	#117	—	2	2	no	—
355	#117	—	2	2	no	—
356	#117	C₂³×C₁₉	1	2	yes	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	4	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	4	no	—
365	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
369	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
370	C₄⋊C₈	—	2	2	no	—
371	C₄⋊C₈	—	2	2	no	—
372	#104	—	2	8	no	—
373	#102	—	2	4	no	—
374	#102	—	2	4	no	—
375	#100	—	2	4	no	—
376	#95	—	2	1	no	—
377	C₁₉	#32920	1	1	yes	characteristic, direct product factor, Sylow
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
381	#41	—	2	8	no	—
382	#41	—	2	8	no	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	#41	C₂×D₄×C₁₉	1	4	yes	—
386	#41	#41×C₁₉	1	4	yes	—
387	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	8	no	—
390	C₂×D₄	—	2	8	no	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	4	8	no	—
402	C₂×D₄	—	4	8	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	4	1	no	—
406	C₂×D₄	—	8	2	no	—
407	C₂×D₄	—	8	4	no	—
408	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
409	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
410	C₂×D₄	#41×C₁₉	1	2	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	8	4	no	—
423	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
427	SD₁₆	—	4	8	no	—
428	D₈	—	4	8	no	—
429	M₁₆	—	2	4	no	—
430	M₁₆	—	2	4	no	—
431	C₂×C₈	—	2	4	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
438	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	4	8	no	—
446	C₄²	—	2	4	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	C₂×D₄×C₁₉	1	2	yes	—
453	C₄²	C₂×D₄×C₁₉	1	2	yes	—
454	C₂³	—	2	8	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	4	no	—
461	C₂³	—	4	4	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	8	2	no	—
466	C₂³	—	8	2	no	—
467	C₂³	C₁₉×#121	1	4	yes	—
468	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
469	Q₈	—	2	2	no	—
470	Q₈	C₁₉×#121	1	4	yes	complemented
471	D₄	—	2	16	no	—
472	D₄	—	2	4	no	—
473	D₄	—	2	4	no	—
474	D₄	—	2	4	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	4	no	—
477	D₄	—	4	4	no	—
478	D₄	—	4	4	no	—
479	D₄	—	8	2	no	—
480	D₄	—	8	4	no	—
481	D₄	—	8	16	no	—
482	D₄	—	8	2	no	—
483	D₄	C₁₉×#121	1	4	yes	complemented
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	8	2	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	—	8	4	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	—	8	2	no	—
504	C₂×C₄	C₁₉×#120	1	2	yes	—
505	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
506	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
509	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
510	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
511	C₈	—	4	4	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	4	no	—
523	C₂²	—	8	4	no	—
524	C₂²	—	8	8	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
529	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
530	C₂²	C₁₉×#525	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	4	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	C₁₉×#453	1	2	yes	complemented
539	C₄	C₂×C₁₉×#121	1	2	yes	—
540	C₄	C₁₉×#525	1	2	yes	—
541	C₂	—	2	1	no	—
542	C₂	—	2	1	no	—
543	C₂	—	4	4	no	—
544	C₂	—	4	4	no	—
545	C₂	—	16	2	no	—
546	C₂	C₁₉×#2847	1	1	yes	characteristic
547	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
548	C₂	C₁₉×#3021	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 ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₉×H(5,𝔽₂)	C₂	semidirect
2. C₁₉×#3038	C₂	semidirect
3. C₂×C₁₉×#453	C₂	semidirect
4. C₁₉×#2541	C₂	semidirect
5. C₁₉×#1887	C₂	semidirect
6. C₁₉×#1883	C₂	semidirect
7. C₁₉×#1806	C₂	semidirect
8. C₁₉×#1800	C₂	semidirect
12. C₂×C₁₉×#127	C₂²	semidirect
29. C₁₉×#423	C₂²	semidirect
31. C₁₉×#418	C₂²	semidirect
34. C₁₉×#390	C₂²	semidirect
35. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
36. C₁₉×#343	C₂²	semidirect
37. C₁₉×#339	C₂²	semidirect
40. C₁₉×H(5,𝔽₂)	D₄	semidirect
63. C₄×Q₈×C₁₉	D₄	semidirect
64. C₄×Q₈×C₁₉	D₄	semidirect
77. C₄×D₄×C₁₉	D₄	semidirect
78. C₄×D₄×C₁₉	D₄	semidirect
179. #32920	C₁₉	direct (N × H)
196. Q₈×C₁₉	#121	semidirect
209. D₄×C₁₉	#121	semidirect
238. C₄×H(5,𝔽₂)	C₂×C₁₉	semidirect
239. #3038	C₂×C₁₉	semidirect
240. C₂×#453	C₂×C₁₉	semidirect
241. #2541	C₂×C₁₉	semidirect
242. #1887	C₂×C₁₉	semidirect
243. #1883	C₂×C₁₉	semidirect
244. #1806	C₂×C₁₉	semidirect
245. #1800	C₂×C₁₉	semidirect
272. C₄×C₁₉	#453	semidirect
278. C₂×#127	C₂²×C₁₉	semidirect
295. #423	C₂²×C₁₉	semidirect
297. #418	C₂²×C₁₉	semidirect
300. #390	C₂²×C₁₉	semidirect
301. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
302. #343	C₂²×C₁₉	semidirect
303. #339	C₂²×C₁₉	semidirect
314. H(5,𝔽₂)	D₄×C₁₉	semidirect
337. C₄×Q₈	D₄×C₁₉	semidirect
338. C₄×Q₈	D₄×C₁₉	semidirect
351. C₄×D₄	D₄×C₁₉	semidirect
352. C₄×D₄	D₄×C₁₉	semidirect
377. C₁₉	#32920	direct (N × H)
470. Q₈	C₁₉×#121	semidirect
483. D₄	C₁₉×#121	semidirect
538. C₄	C₁₉×#453	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₉×H(5,𝔽₂)	2
C₁₉×#3038	2
C₂×C₁₉×#453	2
C₁₉×#2541	2
C₁₉×#1887	2
C₁₉×#1883	2
C₁₉×#1806	2
C₁₉×#1800	2
#32920	19

Subgroups — C19×#32920 #18038879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32920 #18038879