Subgroups — C₁₉×#17764 #18023723

Order 4864.

964 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1560	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1559	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1551	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1550	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1540	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#131	—	2	1	no	—
13	C₁₉×#556	C₄	1	2	yes	—
14	C₁₉×#555	—	2	1	no	—
15	C₁₉×#554	—	2	1	no	—
16	C₁₉×#553	—	2	2	no	—
17	C₁₉×#548	C₄	1	4	yes	—
18	C₁₉×#547	C₄	1	2	yes	—
19	C₁₉×#542	—	2	2	no	—
20	C₁₉×#537	—	2	1	no	—
21	C₁₉×#533	C₂²	1	2	yes	—
22	C₁₉×#532	C₂²	1	2	yes	—
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₉×#520	—	2	1	no	—
26	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#446	—	2	1	no	—
28	C₁₉×#436	—	2	1	no	—
29	C₁₉×#435	—	2	2	no	—
30	C₁₉×#432	C₂²	1	2	yes	—
31	C₁₉×#431	C₂²	1	1	yes	characteristic
32	C₁₉×#424	—	2	1	no	—
33	C₁₉×#424	—	2	2	no	—
34	C₁₉×#423	C₂²	1	2	yes	—
35	C₁₉×#423	C₂²	1	1	yes	characteristic
36	C₁₉×#423	C₂²	1	2	yes	—
37	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
40	C₁₉×#333	C₂²	1	2	yes	—
41	C₁₉×#333	C₂²	1	2	yes	—
42	C₁₉×#333	C₂²	1	2	yes	—
43	C₁₉×#333	C₂²	1	2	yes	—
44	C₁₉×#332	C₂²	1	1	yes	characteristic
45	C₁₉×#332	C₂²	1	1	yes	characteristic
46	C₁₉×#332	C₂²	1	2	yes	—
47	C₁₉×#331	C₂²	1	1	yes	characteristic
48	C₁₉×#331	C₂²	1	1	yes	characteristic
49	C₁₉×#331	C₂²	1	2	yes	—
50	C₂×#41×C₁₉	—	2	1	no	—
51	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
52	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
53	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
54	C₁₉×#131	—	4	4	no	—
55	C₂×M₁₆×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	2	no	—
58	C₂²×C₈×C₁₉	—	2	2	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₂²×C₈×C₁₉	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
64	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₉×#127	C₂³	1	1	yes	characteristic
67	C₁₉×#126	—	2	4	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#124	—	2	4	no	—
70	C₁₉×#124	—	2	1	no	—
71	C₁₉×#124	C₂×C₄	1	4	yes	—
72	C₁₉×#123	—	2	4	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	4	no	—
76	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	2	4	no	—
79	C₁₉×#121	—	2	2	no	—
80	C₁₉×#121	—	2	1	no	—
81	C₁₉×#121	—	2	2	no	—
82	C₁₉×#121	C₂×C₄	1	2	yes	—
83	C₄×Q₈×C₁₉	—	2	2	no	—
84	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
85	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
87	C₄×D₄×C₁₉	—	2	4	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	2	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
92	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
93	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
94	C₄×D₄×C₁₉	D₄	1	2	yes	—
95	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	D₄	1	1	yes	characteristic
99	C₁₉×#117	D₄	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
105	C₁₉×C₄⋊C₈	—	2	2	no	—
106	C₁₉×C₄⋊C₈	—	2	1	no	—
107	C₁₉×C₄⋊C₈	—	2	1	no	—
108	C₁₉×C₄⋊C₈	—	2	2	no	—
109	C₁₉×C₄⋊C₈	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	2	no	—
111	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
114	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
115	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₂²⋊C₈	—	2	1	no	—
118	C₁₉×C₂²⋊C₈	—	2	2	no	—
119	C₁₉×#97	—	2	2	no	—
120	C₄×C₈×C₁₉	—	2	1	no	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	4	2	no	—
124	#41×C₁₉	—	4	2	no	—
125	#41×C₁₉	—	8	4	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	—	8	2	no	—
129	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
136	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
137	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	M₁₆×C₁₉	—	4	4	no	—
148	M₁₆×C₁₉	—	4	2	no	—
149	M₁₆×C₁₉	—	8	2	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	4	4	no	—
157	C₂×C₈×C₁₉	—	4	2	no	—
158	C₂×C₈×C₁₉	—	8	1	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	4	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	4	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
170	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
171	C₂²⋊C₄×C₁₉	—	2	4	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	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
177	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
178	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
179	C₄²×C₁₉	—	2	4	no	—
180	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
182	C₄²×C₁₉	C₂×D₄	1	2	yes	—
183	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₉	C₂×D₄	1	2	yes	—
185	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
187	#17764	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₁₉	—	2	2	no	—
189	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	Q₈×C₁₉	—	2	2	no	—
192	Q₈×C₁₉	—	4	4	no	—
193	Q₈×C₁₉	—	4	1	no	—
194	Q₈×C₁₉	—	4	1	no	—
195	Q₈×C₁₉	—	8	2	no	—
196	D₄×C₁₉	—	2	4	no	—
197	D₄×C₁₉	—	2	2	no	—
198	D₄×C₁₉	—	4	2	no	—
199	D₄×C₁₉	—	4	4	no	—
200	D₄×C₁₉	—	4	1	no	—
201	D₄×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	4	1	no	—
204	D₄×C₁₉	—	8	4	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	4	no	—
216	C₂×C₄×C₁₉	—	8	4	no	—
217	C₂×C₄×C₁₉	—	8	2	no	—
218	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
221	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
225	C₂×C₄×C₁₉	#137	1	2	yes	—
226	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
229	C₈×C₁₉	—	4	1	no	—
230	C₈×C₁₉	—	4	2	no	—
231	C₈×C₁₉	—	4	1	no	—
232	C₈×C₁₉	—	4	2	no	—
233	C₈×C₁₉	—	4	1	no	—
234	C₈×C₁₉	—	4	1	no	—
235	#3511	C₂×C₁₉	1	1	yes	characteristic
236	#2989	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#2906	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#1560	C₂×C₁₉	1	2	yes	complemented
239	#1559	C₂×C₁₉	1	2	yes	complemented
240	#1551	C₂×C₁₉	1	2	yes	complemented
241	#1550	C₂×C₁₉	1	2	yes	complemented
242	#1548	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#1547	C₂×C₁₉	1	1	yes	characteristic, complemented
244	C₂×#333	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#1540	C₂×C₁₉	1	1	yes	characteristic, complemented
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	2	no	—
249	C₂²×C₁₉	—	2	2	no	—
250	C₂²×C₁₉	—	2	2	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	#417	1	2	yes	—
255	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
256	C₄×C₁₉	—	2	1	no	—
257	C₄×C₁₉	—	2	2	no	—
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	2	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	2	no	—
262	C₄×C₁₉	—	4	4	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	#417	1	2	yes	—
265	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
266	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
267	C₄×C₁₉	#577	1	1	yes	characteristic
268	C₄×C₁₉	#578	1	1	yes	characteristic
269	C₂×#131	—	2	1	no	—
270	#556	C₄×C₁₉	1	2	yes	—
271	#555	—	2	1	no	—
272	#554	—	2	1	no	—
273	#553	—	2	2	no	—
274	#548	C₄×C₁₉	1	4	yes	—
275	#547	C₄×C₁₉	1	2	yes	—
276	#542	—	2	2	no	—
277	#537	—	2	1	no	—
278	#533	C₂²×C₁₉	1	2	yes	—
279	#532	C₂²×C₁₉	1	2	yes	—
280	#532	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
282	#520	—	2	1	no	—
283	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
284	#446	—	2	1	no	—
285	#436	—	2	1	no	—
286	#435	—	2	2	no	—
287	#432	C₂²×C₁₉	1	2	yes	—
288	#431	C₂²×C₁₉	1	1	yes	characteristic
289	#424	—	2	1	no	—
290	#424	—	2	2	no	—
291	#423	C₂²×C₁₉	1	1	yes	characteristic
292	#423	C₂²×C₁₉	1	2	yes	—
293	#423	C₂²×C₁₉	1	2	yes	—
294	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
297	#333	C₂²×C₁₉	1	2	yes	—
298	#333	C₂²×C₁₉	1	2	yes	—
299	#333	C₂²×C₁₉	1	2	yes	—
300	#333	C₂²×C₁₉	1	2	yes	—
301	#332	C₂²×C₁₉	1	1	yes	characteristic
302	#332	C₂²×C₁₉	1	1	yes	characteristic
303	#332	C₂²×C₁₉	1	2	yes	—
304	#331	C₂²×C₁₉	1	1	yes	characteristic
305	#331	C₂²×C₁₉	1	1	yes	characteristic
306	#331	C₂²×C₁₉	1	2	yes	—
307	C₂×C₁₉	—	2	2	no	—
308	C₂×C₁₉	—	4	2	no	—
309	C₂×C₁₉	—	8	2	no	—
310	C₂×C₁₉	#2888	1	1	yes	characteristic
311	C₂×C₁₉	C₂×#417	1	1	yes	characteristic
312	C₂×C₁₉	#2898	1	1	yes	characteristic
313	C₂×#41	—	2	1	no	—
314	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
315	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
316	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
317	#131	—	4	4	no	—
318	C₂×M₁₆	—	2	2	no	—
319	C₂×M₁₆	—	2	1	no	—
320	C₂×M₁₆	—	2	2	no	—
321	C₂²×C₈	—	2	2	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	—	2	1	no	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
327	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
328	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
329	#127	C₂³×C₁₉	1	1	yes	characteristic
330	#126	—	2	4	no	—
331	#125	—	2	2	no	—
332	#124	—	2	4	no	—
333	#124	—	2	1	no	—
334	#124	C₂×C₄×C₁₉	1	4	yes	—
335	#123	—	2	4	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
340	#121	—	2	2	no	—
341	#121	—	2	4	no	—
342	#121	—	2	2	no	—
343	#121	—	2	1	no	—
344	#121	—	2	2	no	—
345	#121	C₂×C₄×C₁₉	1	2	yes	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
348	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
349	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
350	C₄×D₄	—	2	4	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
355	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
356	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
357	C₄×D₄	D₄×C₁₉	1	2	yes	—
358	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
359	#117	—	2	2	no	—
360	#117	—	2	2	no	—
361	#117	D₄×C₁₉	1	1	yes	characteristic
362	#117	D₄×C₁₉	1	2	yes	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	—	2	2	no	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	2	no	—
374	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
375	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
377	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
378	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
379	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	—	2	2	no	—
382	#97	—	2	2	no	—
383	C₄×C₈	—	2	1	no	—
384	C₁₉	#17764	1	1	yes	characteristic, direct product factor, Sylow
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	4	2	no	—
388	#41	—	4	2	no	—
389	#41	—	8	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	8	2	no	—
393	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
394	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
400	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
401	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	M₁₆	—	4	4	no	—
412	M₁₆	—	4	2	no	—
413	M₁₆	—	8	2	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	4	4	no	—
421	C₂×C₈	—	4	2	no	—
422	C₂×C₈	—	8	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
431	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
432	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
433	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
434	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
441	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
442	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
443	C₄²	—	2	4	no	—
444	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
445	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
446	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₁₉	1	2	yes	—
448	C₄²	C₂×D₄×C₁₉	1	2	yes	—
449	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
451	C₂³	—	2	2	no	—
452	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
453	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	Q₈	—	4	4	no	—
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	8	2	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	4	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	1	no	—
466	D₄	—	4	1	no	—
467	D₄	—	8	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
482	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
483	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
484	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
485	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
486	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
487	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
488	C₂×C₄	C₁₉×#137	1	2	yes	—
489	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
492	C₈	—	4	1	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	1	no	—
495	C₈	—	4	2	no	—
496	C₈	—	4	1	no	—
497	C₈	—	4	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	C₁₉×#417	1	2	yes	—
507	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
508	C₄	—	2	1	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	2	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	2	no	—
516	C₄	C₁₉×#417	1	2	yes	—
517	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
518	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
519	C₄	C₁₉×#577	1	1	yes	characteristic
520	C₄	C₁₉×#578	1	1	yes	characteristic
521	C₂	—	2	2	no	—
522	C₂	—	4	2	no	—
523	C₂	—	8	2	no	—
524	C₂	C₁₉×#2888	1	1	yes	characteristic
525	C₂	C₂×C₁₉×#417	1	1	yes	characteristic
526	C₂	C₁₉×#2898	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3511	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2989	C₂	semidirect
3. C₁₉×#2906	C₂	semidirect
4. C₁₉×#1560	C₂	semidirect
5. C₁₉×#1559	C₂	semidirect
6. C₁₉×#1551	C₂	semidirect
7. C₁₉×#1550	C₂	semidirect
8. C₁₉×#1548	C₂	semidirect
9. C₁₉×#1547	C₂	semidirect
10. C₂×C₁₉×#333	C₂	semidirect
11. C₁₉×#1540	C₂	semidirect
187. #17764	C₁₉	direct (N × H)
236. #2989	C₂×C₁₉	semidirect
237. #2906	C₂×C₁₉	semidirect
238. #1560	C₂×C₁₉	semidirect
239. #1559	C₂×C₁₉	semidirect
240. #1551	C₂×C₁₉	semidirect
241. #1550	C₂×C₁₉	semidirect
242. #1548	C₂×C₁₉	semidirect
243. #1547	C₂×C₁₉	semidirect
244. C₂×#333	C₂×C₁₉	semidirect
245. #1540	C₂×C₁₉	semidirect
384. C₁₉	#17764	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×#3511	2
C₁₉×#2989	2
C₁₉×#2906	2
C₁₉×#1560	2
C₁₉×#1559	2
C₁₉×#1551	2
C₁₉×#1550	2
C₁₉×#1548	2
C₁₉×#1547	2
C₂×C₁₉×#333	2
C₁₉×#1540	2
#17764	19

Subgroups — C19×#17764 #18023723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17764 #18023723