Subgroups — C₁₉×#32759 #18038718

Order 4864.

978 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2073	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2072	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2071	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2012	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2000	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1999	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#121	—	2	1	no	—
18	C₂×C₁₉×#121	—	2	1	no	—
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#121	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×#102	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₁₉×#391	C₂²	1	1	yes	characteristic
28	C₁₉×#390	—	2	1	no	—
29	C₁₉×#390	—	2	1	no	—
30	C₁₉×#390	C₂²	1	1	yes	characteristic
31	C₁₉×#390	C₂²	1	2	yes	—
32	C₁₉×#388	—	2	1	no	—
33	C₁₉×#388	—	2	1	no	—
34	C₁₉×#386	—	2	1	no	—
35	C₁₉×#386	—	2	1	no	—
36	C₁₉×#384	C₂²	1	1	yes	characteristic
37	C₁₉×#382	C₂²	1	1	yes	characteristic
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	1	yes	characteristic
41	C₁₉×#336	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	—	2	2	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₉	—	4	2	no	—
54	C₂×SD₁₆×C₁₉	—	4	2	no	—
55	C₂×SD₁₆×C₁₉	—	4	2	no	—
56	C₂×D₈×C₁₉	—	4	2	no	—
57	C₂×D₈×C₁₉	—	4	2	no	—
58	C₂×D₈×C₁₉	—	4	2	no	—
59	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
61	C₁₉×#127	—	4	2	no	—
62	C₁₉×#124	—	4	2	no	—
63	C₁₉×C₂²⋊Q₈	—	4	2	no	—
64	C₁₉×#121	—	4	2	no	—
65	C₁₉×#121	—	4	2	no	—
66	C₁₉×#121	—	4	2	no	—
67	C₁₉×#121	—	4	4	no	—
68	C₁₉×#121	—	4	4	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	—	4	2	no	—
85	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
89	C₁₉×#103	—	4	2	no	—
90	C₁₉×#102	—	4	2	no	—
91	C₁₉×#102	—	4	2	no	—
92	C₁₉×#102	—	4	2	no	—
93	C₁₉×C₂²⋊C₈	—	4	2	no	—
94	C₁₉×#95	—	2	1	no	—
95	C₁₉×#95	—	2	1	no	—
96	C₁₉×#95	—	2	1	no	—
97	C₁₉×#95	—	2	1	no	—
98	C₂⁴×C₁₉	—	2	1	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	4	2	no	—
116	C₂×D₄×C₁₉	—	4	2	no	—
117	C₂×D₄×C₁₉	—	4	2	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	—	4	2	no	—
120	C₂×D₄×C₁₉	—	4	4	no	—
121	C₂×D₄×C₁₉	—	4	4	no	—
122	C₂×D₄×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	—	4	4	no	—
124	C₂×D₄×C₁₉	—	4	2	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	—	4	1	no	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
147	SD₁₆×C₁₉	—	4	8	no	—
148	D₈×C₁₉	—	4	8	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	4	2	no	—
160	C₄⋊C₄×C₁₉	—	4	2	no	—
161	C₄⋊C₄×C₁₉	—	4	2	no	—
162	C₂²⋊C₄×C₁₉	—	4	4	no	—
163	C₂²⋊C₄×C₁₉	—	4	2	no	—
164	C₂²⋊C₄×C₁₉	—	4	4	no	—
165	C₂²⋊C₄×C₁₉	—	4	4	no	—
166	C₂²⋊C₄×C₁₉	—	4	2	no	—
167	C₂²⋊C₄×C₁₉	—	4	2	no	—
168	C₂²⋊C₄×C₁₉	—	4	2	no	—
169	C₂²⋊C₄×C₁₉	—	4	2	no	—
170	C₂²⋊C₄×C₁₉	—	4	2	no	—
171	C₄²×C₁₉	—	2	2	no	—
172	C₄²×C₁₉	—	2	2	no	—
173	C₄²×C₁₉	—	4	1	no	—
174	C₄²×C₁₉	—	4	1	no	—
175	#32759	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	—	2	1	no	—
178	C₂³×C₁₉	—	2	1	no	—
179	C₂³×C₁₉	—	2	1	no	—
180	C₂³×C₁₉	—	2	1	no	—
181	C₂³×C₁₉	—	2	1	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	—	4	1	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	1	no	—
193	C₂³×C₁₉	—	4	1	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	1	no	—
196	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
197	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₁₉	—	4	2	no	—
199	Q₈×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	4	2	no	—
201	D₄×C₁₉	—	4	2	no	—
202	D₄×C₁₉	—	4	2	no	—
203	D₄×C₁₉	—	4	2	no	—
204	D₄×C₁₉	—	4	2	no	—
205	D₄×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	8	4	no	—
207	D₄×C₁₉	—	8	4	no	—
208	D₄×C₁₉	—	8	4	no	—
209	D₄×C₁₉	—	8	8	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	4	4	no	—
224	C₂×C₄×C₁₉	—	4	4	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	#135	1	2	yes	—
240	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
241	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
242	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
243	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
244	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
245	C₈×C₁₉	—	4	2	no	—
246	C₈×C₁₉	—	4	2	no	—
247	#2856	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#2850	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#2073	C₂×C₁₉	1	2	yes	complemented
250	#2072	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#2071	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#2014	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#2012	C₂×C₁₉	1	2	yes	complemented
254	#2011	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#2000	C₂×C₁₉	1	2	yes	complemented
256	#1999	C₂×C₁₉	1	2	yes	complemented
257	#1817	C₂×C₁₉	1	1	yes	characteristic, complemented
258	C₂²×C₁₉	—	2	2	no	—
259	C₂²×C₁₉	—	2	2	no	—
260	C₂²×C₁₉	—	2	2	no	—
261	C₂²×C₁₉	—	4	1	no	—
262	C₂²×C₁₉	—	4	1	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	8	2	no	—
266	C₂²×C₁₉	—	8	1	no	—
267	C₂²×C₁₉	—	8	2	no	—
268	C₂²×C₁₉	—	8	1	no	—
269	C₂²×C₁₉	—	8	1	no	—
270	C₂²×C₁₉	—	8	2	no	—
271	C₂²×C₁₉	—	8	2	no	—
272	C₂²×C₁₉	—	8	1	no	—
273	C₂²×C₁₉	—	8	1	no	—
274	C₂²×C₁₉	—	8	2	no	—
275	C₂²×C₁₉	—	8	2	no	—
276	C₂²×C₁₉	—	8	1	no	—
277	C₂²×C₁₉	—	8	1	no	—
278	C₂²×C₁₉	—	8	2	no	—
279	C₂²×C₁₉	#534	1	1	yes	characteristic
280	C₂²×C₁₉	#535	1	1	yes	characteristic
281	C₂²×C₁₉	#535	1	1	yes	characteristic
282	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
283	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₂²×C₁₉	#575	1	1	yes	characteristic
286	C₄×C₁₉	—	2	2	no	—
287	C₄×C₁₉	—	2	2	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	1	no	—
290	C₄×C₁₉	—	4	1	no	—
291	C₄×C₁₉	—	8	1	no	—
292	C₄×C₁₉	—	8	1	no	—
293	C₄×C₁₉	—	8	2	no	—
294	C₄×C₁₉	—	8	1	no	—
295	C₄×C₁₉	#560	1	2	yes	—
296	C₄×C₁₉	#560	1	2	yes	—
297	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
298	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
299	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#121	—	2	1	no	—
303	C₂×#121	—	2	1	no	—
304	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×#121	C₂²×C₁₉	1	2	yes	—
306	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×#103	C₂²×C₁₉	1	2	yes	—
308	C₂×#102	C₂²×C₁₉	1	2	yes	—
309	C₂×#102	C₂²×C₁₉	1	2	yes	—
310	C₂×#102	C₂²×C₁₉	1	2	yes	—
311	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
312	#391	C₂²×C₁₉	1	1	yes	characteristic
313	#390	—	2	1	no	—
314	#390	—	2	1	no	—
315	#390	C₂²×C₁₉	1	1	yes	characteristic
316	#390	C₂²×C₁₉	1	2	yes	—
317	#388	—	2	1	no	—
318	#388	—	2	1	no	—
319	#386	—	2	1	no	—
320	#386	—	2	1	no	—
321	#384	C₂²×C₁₉	1	1	yes	characteristic
322	#382	C₂²×C₁₉	1	1	yes	characteristic
323	#340	C₂²×C₁₉	1	2	yes	—
324	#340	C₂²×C₁₉	1	2	yes	—
325	#336	C₂²×C₁₉	1	1	yes	characteristic
326	#336	C₂²×C₁₉	1	1	yes	characteristic
327	#336	C₂²×C₁₉	1	2	yes	—
328	C₂×C₁₉	—	4	2	no	—
329	C₂×C₁₉	—	16	2	no	—
330	C₂×C₁₉	—	16	1	no	—
331	C₂×C₁₉	#2815	1	1	yes	characteristic
332	C₂×C₁₉	#3188	1	1	yes	characteristic
333	C₂×C₁₉	#3194	1	1	yes	characteristic
334	C₂×C₁₉	#3207	1	1	yes	characteristic
335	C₂×C₁₉	#3212	1	1	yes	characteristic
336	C₂×C₁₉	#3213	1	1	yes	characteristic
337	C₂×C₁₉	#3217	1	1	yes	characteristic
338	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
344	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
345	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
346	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
348	C₂×SD₁₆	—	4	2	no	—
349	C₂×SD₁₆	—	4	2	no	—
350	C₂×SD₁₆	—	4	2	no	—
351	C₂×D₈	—	4	2	no	—
352	C₂×D₈	—	4	2	no	—
353	C₂×D₈	—	4	2	no	—
354	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
355	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
356	#127	—	4	2	no	—
357	#124	—	4	2	no	—
358	C₂²⋊Q₈	—	4	2	no	—
359	#121	—	4	2	no	—
360	#121	—	4	2	no	—
361	#121	—	4	2	no	—
362	#121	—	4	4	no	—
363	#121	—	4	4	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₄²	—	4	2	no	—
380	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
381	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
384	#103	—	4	2	no	—
385	#102	—	4	2	no	—
386	#102	—	4	2	no	—
387	#102	—	4	2	no	—
388	C₂²⋊C₈	—	4	2	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	C₁₉	#32759	1	1	yes	characteristic, direct product factor, Sylow
394	C₂⁴	—	2	1	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	—	4	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	4	1	no	—
435	C₂²×C₄	—	4	1	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
443	SD₁₆	—	4	8	no	—
444	D₈	—	4	8	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₄⋊C₄	—	4	2	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₂²⋊C₄	—	4	4	no	—
459	C₂²⋊C₄	—	4	2	no	—
460	C₂²⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	4	4	no	—
462	C₂²⋊C₄	—	4	2	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	4	1	no	—
470	C₄²	—	4	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	1	no	—
491	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
492	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
493	Q₈	—	4	2	no	—
494	Q₈	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	8	4	no	—
502	D₄	—	8	4	no	—
503	D₄	—	8	4	no	—
504	D₄	—	8	8	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	C₁₉×#135	1	2	yes	—
535	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
536	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
537	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
538	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
540	C₈	—	4	2	no	—
541	C₈	—	4	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	2	no	—
552	C₂²	—	8	1	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	2	no	—
555	C₂²	—	8	2	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	2	no	—
559	C₂²	—	8	2	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	2	no	—
563	C₂²	C₁₉×#534	1	1	yes	characteristic
564	C₂²	C₁₉×#535	1	1	yes	characteristic
565	C₂²	C₁₉×#535	1	1	yes	characteristic
566	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
567	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
568	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
569	C₂²	C₁₉×#575	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	2	no	—
578	C₄	—	8	1	no	—
579	C₄	C₁₉×#560	1	2	yes	—
580	C₄	C₁₉×#560	1	2	yes	—
581	C₂	—	4	2	no	—
582	C₂	—	16	2	no	—
583	C₂	—	16	1	no	—
584	C₂	C₁₉×#2815	1	1	yes	characteristic
585	C₂	C₁₉×#3188	1	1	yes	characteristic
586	C₂	C₁₉×#3194	1	1	yes	characteristic
587	C₂	C₁₉×#3207	1	1	yes	characteristic
588	C₂	C₁₉×#3212	1	1	yes	characteristic
589	C₂	C₁₉×#3213	1	1	yes	characteristic
590	C₂	C₁₉×#3217	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2856	C₂	semidirect
2. C₁₉×#2850	C₂	semidirect
3. C₁₉×#2073	C₂	semidirect
4. C₁₉×#2072	C₂	semidirect
5. C₁₉×#2071	C₂	semidirect
6. C₁₉×#2014	C₂	semidirect
7. C₁₉×#2012	C₂	semidirect
8. C₁₉×#2011	C₂	semidirect
9. C₁₉×#2000	C₂	semidirect
10. C₁₉×#1999	C₂	semidirect
11. C₁₉×#1817	C₂	semidirect
175. #32759	C₁₉	direct (N × H)
247. #2856	C₂×C₁₉	semidirect
248. #2850	C₂×C₁₉	semidirect
249. #2073	C₂×C₁₉	semidirect
250. #2072	C₂×C₁₉	semidirect
251. #2071	C₂×C₁₉	semidirect
252. #2014	C₂×C₁₉	semidirect
253. #2012	C₂×C₁₉	semidirect
254. #2011	C₂×C₁₉	semidirect
255. #2000	C₂×C₁₉	semidirect
256. #1999	C₂×C₁₉	semidirect
257. #1817	C₂×C₁₉	semidirect
393. C₁₉	#32759	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×#2856	2
C₁₉×#2850	2
C₁₉×#2073	2
C₁₉×#2072	2
C₁₉×#2071	2
C₁₉×#2014	2
C₁₉×#2012	2
C₁₉×#2011	2
C₁₉×#2000	2
C₁₉×#1999	2
C₁₉×#1817	2
#32759	19

Subgroups — C19×#32759 #18038718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32759 #18038718