Subgroups — C₁₉×#17752 #18023711

Order 4864.

1064 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#423	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1561	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1560	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1550	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1547	C₂	1	4	yes	maximal, complemented
7	C₂²×M₁₆×C₁₉	—	2	2	no	—
8	C₁₉×#533	C₂²	1	2	yes	—
9	C₁₉×#533	C₂²	1	1	yes	characteristic
10	C₁₉×#532	C₂²	1	1	yes	characteristic
11	C₁₉×#532	C₂²	1	2	yes	—
12	C₁₉×#529	—	2	2	no	—
13	C₁₉×#529	—	2	2	no	—
14	C₁₉×#529	C₄	1	4	yes	—
15	C₁₉×#525	—	2	2	no	—
16	C₁₉×#525	C₄	1	2	yes	—
17	C₄×#41×C₁₉	—	2	2	no	—
18	C₄×#41×C₁₉	C₄	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#423	—	2	2	no	—
21	C₁₉×#423	—	2	2	no	—
22	C₁₉×#423	C₂²	1	4	yes	—
23	C₁₉×#423	C₂²	1	4	yes	—
24	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
26	C₁₉×#333	C₂²	1	4	yes	complemented
27	C₁₉×#332	C₂²	1	8	yes	complemented
28	C₁₉×#331	C₂²	1	4	yes	complemented
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	D₄	1	2	yes	—
33	C₂×M₁₆×C₁₉	—	2	4	no	—
34	C₂×M₁₆×C₁₉	—	2	4	no	—
35	C₂×M₁₆×C₁₉	—	4	8	no	—
36	C₂²×C₈×C₁₉	—	2	4	no	—
37	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
38	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
39	C₁₉×#127	C₂³	1	1	yes	characteristic
40	C₁₉×#126	—	2	4	no	—
41	C₁₉×#125	—	2	2	no	—
42	C₁₉×#125	C₂×C₄	1	2	yes	—
43	C₁₉×#124	—	2	2	no	—
44	C₁₉×#124	C₂×C₄	1	2	yes	—
45	C₁₉×#123	—	2	4	no	—
46	C₁₉×#123	—	2	2	no	—
47	C₁₉×C₂²⋊Q₈	—	2	2	no	—
48	C₁₉×C₂²⋊Q₈	—	2	2	no	—
49	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
50	C₁₉×#121	—	2	2	no	—
51	C₁₉×#121	—	2	2	no	—
52	C₁₉×#121	C₂×C₄	1	4	yes	—
53	C₁₉×#120	—	2	2	no	—
54	C₄×Q₈×C₁₉	—	2	2	no	—
55	C₄×Q₈×C₁₉	—	2	2	no	—
56	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
57	C₄×D₄×C₁₉	—	2	4	no	—
58	C₄×D₄×C₁₉	—	2	4	no	—
59	C₄×D₄×C₁₉	—	2	4	no	—
60	C₄×D₄×C₁₉	—	2	2	no	—
61	C₄×D₄×C₁₉	—	2	2	no	—
62	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
63	C₁₉×#117	—	2	2	no	—
64	C₁₉×#117	—	2	4	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₁₉	D₄	1	2	yes	—
71	C₂×C₄²×C₁₉	D₄	1	2	yes	—
72	C₂×C₄²×C₁₉	D₄	1	2	yes	—
73	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×C₄⋊C₈	—	2	4	no	—
76	C₁₉×C₄⋊C₈	—	2	4	no	—
77	C₁₉×C₄⋊C₈	—	2	4	no	—
78	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
79	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	#41×C₁₉	—	4	4	no	—
81	#41×C₁₉	—	4	4	no	—
82	#41×C₁₉	—	4	4	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	4	2	no	—
94	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	M₁₆×C₁₉	—	4	8	no	—
105	M₁₆×C₁₉	—	4	8	no	—
106	C₂×C₈×C₁₉	—	2	8	no	—
107	C₂×C₈×C₁₉	—	4	8	no	—
108	C₄⋊C₄×C₁₉	—	2	4	no	—
109	C₄⋊C₄×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
114	C₂²⋊C₄×C₁₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₉	—	2	2	no	—
116	C₂²⋊C₄×C₁₉	—	2	4	no	—
117	C₂²⋊C₄×C₁₉	—	2	4	no	—
118	C₂²⋊C₄×C₁₉	—	2	4	no	—
119	C₄²×C₁₉	—	2	4	no	—
120	C₄²×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
125	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
126	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₁₉	C₂×D₄	1	2	yes	—
128	C₄²×C₁₉	C₂×D₄	1	2	yes	—
129	C₄²×C₁₉	C₂×D₄	1	2	yes	—
130	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
131	#17752	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
137	Q₈×C₁₉	—	4	2	no	—
138	Q₈×C₁₉	—	4	2	no	—
139	Q₈×C₁₉	—	4	2	no	—
140	D₄×C₁₉	—	4	2	no	—
141	D₄×C₁₉	—	4	4	no	—
142	D₄×C₁₉	—	4	8	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	—	4	8	no	—
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
166	C₂×C₄×C₁₉	#137	1	4	yes	—
167	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
169	C₈×C₁₉	—	4	8	no	—
170	#3444	C₂×C₁₉	1	1	yes	characteristic
171	C₂×#423	C₂×C₁₉	1	2	yes	complemented
172	#1561	C₂×C₁₉	1	2	yes	complemented
173	#1560	C₂×C₁₉	1	2	yes	complemented
174	#1550	C₂×C₁₉	1	4	yes	complemented
175	#1547	C₂×C₁₉	1	4	yes	complemented
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	4	4	no	—
181	C₂²×C₁₉	—	4	2	no	—
182	C₂²×C₁₉	—	4	4	no	—
183	C₂²×C₁₉	#417	1	4	yes	—
184	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
185	C₄×C₁₉	—	2	2	no	—
186	C₄×C₁₉	—	2	1	no	—
187	C₄×C₁₉	—	2	2	no	—
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	4	2	no	—
190	C₄×C₁₉	—	4	4	no	—
191	C₄×C₁₉	#413	1	2	yes	—
192	C₄×C₁₉	#417	1	4	yes	—
193	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
194	C₄×C₁₉	C₂×#137	1	2	yes	—
195	C₂²×M₁₆	—	2	2	no	—
196	#533	C₂²×C₁₉	1	2	yes	—
197	#533	C₂²×C₁₉	1	1	yes	characteristic
198	#532	C₂²×C₁₉	1	1	yes	characteristic
199	#532	C₂²×C₁₉	1	2	yes	—
200	#529	—	2	2	no	—
201	#529	—	2	2	no	—
202	#529	C₄×C₁₉	1	4	yes	—
203	#525	—	2	2	no	—
204	#525	C₄×C₁₉	1	2	yes	—
205	C₄×#41	—	2	2	no	—
206	C₄×#41	C₄×C₁₉	1	2	yes	—
207	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
208	#423	—	2	2	no	—
209	#423	—	2	2	no	—
210	#423	C₂²×C₁₉	1	4	yes	—
211	#423	C₂²×C₁₉	1	4	yes	—
212	C₂×C₄⋊C₈	—	2	2	no	—
213	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
214	#333	C₂²×C₁₉	1	4	yes	complemented
215	#332	C₂²×C₁₉	1	8	yes	complemented
216	#331	C₂²×C₁₉	1	4	yes	complemented
217	C₂×C₁₉	—	2	4	no	—
218	C₂×C₁₉	—	4	1	no	—
219	C₂×C₁₉	—	8	2	no	—
220	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
221	C₂×C₁₉	C₂×#417	1	2	yes	—
222	C₂×#41	—	2	2	no	—
223	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
224	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
225	C₂³×C₄	D₄×C₁₉	1	2	yes	—
226	C₂×M₁₆	—	2	4	no	—
227	C₂×M₁₆	—	2	4	no	—
228	C₂×M₁₆	—	4	8	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
231	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
232	#127	C₂³×C₁₉	1	1	yes	characteristic
233	#126	—	2	4	no	—
234	#125	—	2	2	no	—
235	#125	C₂×C₄×C₁₉	1	2	yes	—
236	#124	—	2	2	no	—
237	#124	C₂×C₄×C₁₉	1	2	yes	—
238	#123	—	2	4	no	—
239	#123	—	2	2	no	—
240	C₂²⋊Q₈	—	2	2	no	—
241	C₂²⋊Q₈	—	2	2	no	—
242	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
243	#121	—	2	2	no	—
244	#121	—	2	2	no	—
245	#121	C₂×C₄×C₁₉	1	4	yes	—
246	#120	—	2	2	no	—
247	C₄×Q₈	—	2	2	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
250	C₄×D₄	—	2	4	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	—	2	4	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
256	#117	—	2	2	no	—
257	#117	—	2	4	no	—
258	#117	—	2	2	no	—
259	#117	C₂×C₄×C₁₉	1	2	yes	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
263	C₂×C₄²	D₄×C₁₉	1	2	yes	—
264	C₂×C₄²	D₄×C₁₉	1	2	yes	—
265	C₂×C₄²	D₄×C₁₉	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
267	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
268	C₄⋊C₈	—	2	4	no	—
269	C₄⋊C₈	—	2	4	no	—
270	C₄⋊C₈	—	2	4	no	—
271	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
272	C₁₉	#17752	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
274	#41	—	4	4	no	—
275	#41	—	4	4	no	—
276	#41	—	4	4	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
289	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
290	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
291	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
292	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
298	M₁₆	—	4	8	no	—
299	M₁₆	—	4	8	no	—
300	C₂×C₈	—	2	8	no	—
301	C₂×C₈	—	4	8	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
308	C₂²⋊C₄	—	2	4	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	2	2	no	—
315	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
316	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
317	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
318	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
319	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
320	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₁₉	1	2	yes	—
322	C₄²	C₂×D₄×C₁₉	1	2	yes	—
323	C₄²	C₂×D₄×C₁₉	1	2	yes	—
324	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
325	C₂³	—	2	4	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	4	1	no	—
328	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
329	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	8	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
355	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
356	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
357	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
358	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
359	C₂×C₄	C₁₉×#137	1	4	yes	—
360	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
361	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
362	C₈	—	4	8	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	4	no	—
370	C₂²	C₁₉×#417	1	4	yes	—
371	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	4	no	—
378	C₄	C₁₉×#413	1	2	yes	—
379	C₄	C₁₉×#417	1	4	yes	—
380	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
381	C₄	C₂×C₁₉×#137	1	2	yes	—
382	C₂	—	2	4	no	—
383	C₂	—	4	1	no	—
384	C₂	—	8	2	no	—
385	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
386	C₂	C₂×C₁₉×#417	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#423	C₂	semidirect
3. C₁₉×#1561	C₂	semidirect
4. C₁₉×#1560	C₂	semidirect
5. C₁₉×#1550	C₂	semidirect
6. C₁₉×#1547	C₂	semidirect
26. C₁₉×#333	C₂²	semidirect
27. C₁₉×#332	C₂²	semidirect
28. C₁₉×#331	C₂²	semidirect
131. #17752	C₁₉	direct (N × H)
171. C₂×#423	C₂×C₁₉	semidirect
172. #1561	C₂×C₁₉	semidirect
173. #1560	C₂×C₁₉	semidirect
174. #1550	C₂×C₁₉	semidirect
175. #1547	C₂×C₁₉	semidirect
214. #333	C₂²×C₁₉	semidirect
215. #332	C₂²×C₁₉	semidirect
216. #331	C₂²×C₁₉	semidirect
272. C₁₉	#17752	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×#3444	2
C₂×C₁₉×#423	2
C₁₉×#1561	2
C₁₉×#1560	2
C₁₉×#1550	2
C₁₉×#1547	2
#17752	19

Subgroups — C19×#17752 #18023711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17752 #18023711