Subgroups — C₂×C₁₉×#2189 #18039474

Order 4864.

1146 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#135	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2189	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	—	2	1	no	—
10	C₂×C₁₉×#135	—	2	4	no	—
11	C₂×C₁₉×#135	—	2	4	no	—
12	C₂×C₁₉×#135	—	2	2	no	—
13	C₂×C₁₉×#135	C₂²	1	4	yes	—
14	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×SD₁₆×C₁₉	—	2	1	no	—
17	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₉×Q₃₂	—	2	4	no	—
21	C₂×C₁₉×Q₃₂	C₂²	1	4	yes	complemented
22	C₂×C₁₉×SD₃₂	—	2	4	no	—
23	C₂×C₁₉×SD₃₂	C₂²	1	4	yes	complemented
24	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#467	—	2	2	no	—
27	C₁₉×#467	C₂²	1	4	yes	complemented
28	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	—	2	1	no	—
30	C₁₉×#358	C₂²	1	4	yes	complemented
31	C₁₉×#357	C₂²	1	4	yes	complemented
32	C₁₉×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
33	C₂×#41×C₁₉	—	2	8	no	—
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	—	4	4	no	—
36	C₂×#41×C₁₉	—	4	2	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	4	1	no	—
41	C₂³×C₄×C₁₉	—	4	1	no	—
42	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₁₉×#135	—	2	16	no	—
44	C₁₉×#135	—	2	8	no	—
45	C₁₉×#135	—	2	8	no	—
46	C₂×Q₁₆×C₁₉	—	2	1	no	—
47	C₂×Q₁₆×C₁₉	—	2	2	no	—
48	C₂×Q₁₆×C₁₉	—	2	2	no	—
49	C₂×Q₁₆×C₁₉	—	2	2	no	—
50	C₂×Q₁₆×C₁₉	—	2	1	no	—
51	C₂×Q₁₆×C₁₉	D₄	1	4	yes	—
52	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
53	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
54	C₂×SD₁₆×C₁₉	—	2	8	no	—
55	C₂×SD₁₆×C₁₉	—	2	4	no	—
56	C₂×D₈×C₁₉	—	2	1	no	—
57	C₂×D₈×C₁₉	—	2	2	no	—
58	C₂×D₈×C₁₉	D₄	1	4	yes	—
59	C₂×D₈×C₁₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₉	—	2	2	no	—
61	C₂²×C₈×C₁₉	—	2	2	no	—
62	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	D₄	1	2	yes	—
64	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×C₂²⋊Q₈	—	2	4	no	—
67	C₁₉×C₂²⋊Q₈	—	4	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
71	C₁₉×Q₃₂	—	2	8	no	—
72	C₁₉×SD₃₂	—	2	8	no	—
73	C₂×C₁₆×C₁₉	—	2	2	no	—
74	C₂×C₁₆×C₁₉	—	2	2	no	—
75	C₂×C₁₆×C₁₉	C₂³	1	2	yes	—
76	C₂×C₁₆×C₁₉	C₂³	1	2	yes	—
77	C₁₉×#107	—	2	1	no	—
78	C₁₉×#107	C₂³	1	2	yes	—
79	C₁₉×#103	—	2	4	no	—
80	C₂⁴×C₁₉	—	4	1	no	—
81	C₂⁴×C₁₉	D₈	1	1	yes	characteristic
82	#41×C₁₉	—	2	16	no	—
83	#41×C₁₉	—	4	8	no	—
84	#41×C₁₉	—	4	16	no	—
85	C₂×Q₈×C₁₉	—	2	4	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	4	1	no	—
89	C₂×Q₈×C₁₉	—	4	1	no	—
90	C₂×Q₈×C₁₉	—	4	2	no	—
91	C₂×Q₈×C₁₉	—	4	2	no	—
92	C₂×Q₈×C₁₉	—	4	2	no	—
93	C₂×D₄×C₁₉	—	2	4	no	—
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	4	8	no	—
96	C₂×D₄×C₁₉	—	4	4	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	4	8	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	4	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	D₈	1	2	yes	—
107	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	Q₁₆×C₁₉	—	2	4	no	—
111	Q₁₆×C₁₉	—	2	2	no	—
112	Q₁₆×C₁₉	—	2	2	no	—
113	Q₁₆×C₁₉	—	2	2	no	—
114	Q₁₆×C₁₉	—	4	2	no	—
115	Q₁₆×C₁₉	C₂×D₄	1	4	yes	—
116	SD₁₆×C₁₉	—	2	16	no	—
117	D₈×C₁₉	—	2	4	no	—
118	D₈×C₁₉	—	2	2	no	—
119	D₈×C₁₉	C₂×D₄	1	4	yes	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	4	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	4	4	no	—
132	C₂²⋊C₄×C₁₉	—	4	4	no	—
133	C₁₆×C₁₉	—	2	2	no	—
134	C₁₆×C₁₉	—	2	2	no	—
135	C₂×#2189	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	—	8	2	no	—
142	C₂³×C₁₉	—	8	2	no	—
143	C₂³×C₁₉	C₂×D₈	1	2	yes	—
144	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
145	Q₈×C₁₉	—	2	4	no	—
146	Q₈×C₁₉	—	4	2	no	—
147	Q₈×C₁₉	—	4	4	no	—
148	Q₈×C₁₉	—	4	2	no	—
149	Q₈×C₁₉	—	4	2	no	—
150	Q₈×C₁₉	—	8	2	no	—
151	D₄×C₁₉	—	2	4	no	—
152	D₄×C₁₉	—	4	16	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	4	16	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	8	2	no	—
165	C₂×C₄×C₁₉	—	8	2	no	—
166	C₂×C₄×C₁₉	#120	1	2	yes	—
167	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
170	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
171	C₈×C₁₉	—	2	2	no	—
172	C₈×C₁₉	#120	1	2	yes	—
173	C₈×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	C₈×C₁₉	C₂²×D₄	1	1	yes	characteristic
175	C₂²×#135	C₂×C₁₉	1	1	yes	characteristic
176	C₂²×Q₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
177	C₂²×SD₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
178	C₂×#467	C₂×C₁₉	1	1	yes	characteristic, complemented
179	#2189	C₂×C₁₉	1	8	yes	direct product factor
180	C₂×#358	C₂×C₁₉	1	1	yes	characteristic, complemented
181	C₂×#357	C₂×C₁₉	1	1	yes	characteristic, complemented
182	C₂×C₂²⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
183	C₂²×C₁₉	—	2	2	no	—
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	4	4	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	8	2	no	—
189	C₂²×C₁₉	—	8	2	no	—
190	C₂²×C₁₉	—	8	8	no	—
191	C₂²×C₁₉	#447	1	2	yes	—
192	C₂²×C₁₉	#508	1	2	yes	—
193	C₂²×C₁₉	#510	1	2	yes	—
194	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	4	4	no	—
197	C₄×C₁₉	—	8	2	no	—
198	C₄×C₁₉	—	8	2	no	—
199	C₄×C₁₉	#447	1	2	yes	—
200	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
201	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂²×#41	—	2	1	no	—
203	C₂×#135	—	2	4	no	—
204	C₂×#135	—	2	4	no	—
205	C₂×#135	—	2	2	no	—
206	C₂×#135	C₂²×C₁₉	1	4	yes	—
207	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
208	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
209	C₂²×SD₁₆	—	2	1	no	—
210	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
211	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×C₂²⋊Q₈	—	2	1	no	—
213	C₂×Q₃₂	—	2	4	no	—
214	C₂×Q₃₂	C₂²×C₁₉	1	4	yes	complemented
215	C₂×SD₃₂	—	2	4	no	—
216	C₂×SD₃₂	C₂²×C₁₉	1	4	yes	complemented
217	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
218	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
219	#467	—	2	2	no	—
220	#467	C₂²×C₁₉	1	4	yes	complemented
221	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
222	C₂×#103	—	2	1	no	—
223	#358	C₂²×C₁₉	1	4	yes	complemented
224	#357	C₂²×C₁₉	1	4	yes	complemented
225	C₂²⋊C₁₆	C₂²×C₁₉	1	4	yes	complemented
226	C₂×C₁₉	—	4	2	no	—
227	C₂×C₁₉	—	8	4	no	—
228	C₂×C₁₉	#2189	1	4	yes	direct product factor
229	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
230	C₂×C₁₉	C₂×#508	1	1	yes	characteristic
231	C₂×C₁₉	C₂×#510	1	1	yes	characteristic
232	C₂×#41	—	2	8	no	—
233	C₂×#41	—	2	4	no	—
234	C₂×#41	—	4	4	no	—
235	C₂×#41	—	4	2	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	4	1	no	—
240	C₂³×C₄	—	4	1	no	—
241	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
242	#135	—	2	16	no	—
243	#135	—	2	8	no	—
244	#135	—	2	8	no	—
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×Q₁₆	—	2	2	no	—
247	C₂×Q₁₆	—	2	2	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	D₄×C₁₉	1	4	yes	—
251	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
252	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
253	C₂×SD₁₆	—	2	8	no	—
254	C₂×SD₁₆	—	2	4	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	2	no	—
257	C₂×D₈	D₄×C₁₉	1	4	yes	—
258	C₂×D₈	C₂³×C₁₉	1	2	yes	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
262	C₂²×C₈	D₄×C₁₉	1	2	yes	—
263	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
264	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
265	C₂²⋊Q₈	—	2	4	no	—
266	C₂²⋊Q₈	—	4	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	4	1	no	—
269	C₂×C₂²⋊C₄	—	4	1	no	—
270	Q₃₂	—	2	8	no	—
271	SD₃₂	—	2	8	no	—
272	C₂×C₁₆	—	2	2	no	—
273	C₂×C₁₆	—	2	2	no	—
274	C₂×C₁₆	C₂³×C₁₉	1	2	yes	—
275	C₂×C₁₆	C₂³×C₁₉	1	2	yes	—
276	#107	—	2	1	no	—
277	#107	C₂³×C₁₉	1	2	yes	—
278	#103	—	2	4	no	—
279	C₁₉	C₂×#2189	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	—	4	1	no	—
281	C₂⁴	D₈×C₁₉	1	1	yes	characteristic
282	#41	—	2	16	no	—
283	#41	—	4	16	no	—
284	#41	—	4	8	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	8	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	4	8	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	D₈×C₁₉	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
310	Q₁₆	—	2	4	no	—
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	2	2	no	—
313	Q₁₆	—	2	2	no	—
314	Q₁₆	—	4	2	no	—
315	Q₁₆	C₂×D₄×C₁₉	1	4	yes	—
316	SD₁₆	—	2	16	no	—
317	D₈	—	2	4	no	—
318	D₈	—	2	2	no	—
319	D₈	C₂×D₄×C₁₉	1	4	yes	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
328	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₁₆	—	2	2	no	—
334	C₁₆	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	8	2	no	—
341	C₂³	—	8	2	no	—
342	C₂³	C₂×D₈×C₁₉	1	2	yes	—
343	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	4	4	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	8	2	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	16	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	16	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	C₁₉×#120	1	2	yes	—
366	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
367	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
368	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
369	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	C₁₉×#120	1	2	yes	—
372	C₈	C₂²×D₄×C₁₉	1	1	yes	characteristic
373	C₈	C₂²×D₄×C₁₉	1	1	yes	characteristic
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	8	8	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	C₁₉×#447	1	2	yes	—
383	C₂²	C₁₉×#508	1	2	yes	—
384	C₂²	C₁₉×#510	1	2	yes	—
385	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	4	4	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	2	no	—
390	C₄	C₁₉×#447	1	2	yes	—
391	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
392	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₂	—	4	2	no	—
394	C₂	—	8	4	no	—
395	C₂	C₁₉×#2189	1	4	yes	direct product factor
396	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
397	C₂	C₂×C₁₉×#508	1	1	yes	characteristic
398	C₂	C₂×C₁₉×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#135	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×Q₃₂	C₂	semidirect
3. C₂²×C₁₉×SD₃₂	C₂	semidirect
4. C₂×C₁₉×#467	C₂	semidirect
5. C₁₉×#2189	C₂	direct (N × H)
6. C₂×C₁₉×#358	C₂	semidirect
7. C₂×C₁₉×#357	C₂	semidirect
8. C₂×C₁₉×C₂²⋊C₁₆	C₂	semidirect
21. C₂×C₁₉×Q₃₂	C₂²	semidirect
23. C₂×C₁₉×SD₃₂	C₂²	semidirect
27. C₁₉×#467	C₂²	semidirect
30. C₁₉×#358	C₂²	semidirect
31. C₁₉×#357	C₂²	semidirect
32. C₁₉×C₂²⋊C₁₆	C₂²	semidirect
135. C₂×#2189	C₁₉	direct (N × H)
176. C₂²×Q₃₂	C₂×C₁₉	semidirect
177. C₂²×SD₃₂	C₂×C₁₉	semidirect
178. C₂×#467	C₂×C₁₉	semidirect
179. #2189	C₂×C₁₉	direct (N × H)
180. C₂×#358	C₂×C₁₉	semidirect
181. C₂×#357	C₂×C₁₉	semidirect
182. C₂×C₂²⋊C₁₆	C₂×C₁₉	semidirect
214. C₂×Q₃₂	C₂²×C₁₉	semidirect
216. C₂×SD₃₂	C₂²×C₁₉	semidirect
220. #467	C₂²×C₁₉	semidirect
223. #358	C₂²×C₁₉	semidirect
224. #357	C₂²×C₁₉	semidirect
225. C₂²⋊C₁₆	C₂²×C₁₉	semidirect
228. C₂×C₁₉	#2189	direct (N × H)
279. C₁₉	C₂×#2189	direct (N × H)
395. C₂	C₁₉×#2189	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#135	2
C₂²×C₁₉×Q₃₂	2
C₂²×C₁₉×SD₃₂	2
C₂×C₁₉×#467	2
C₁₉×#2189	2
C₂×C₁₉×#358	2
C₂×C₁₉×#357	2
C₂×C₁₉×C₂²⋊C₁₆	2
C₂×#2189	19

Subgroups — C2×C19×#2189 #18039474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2189 #18039474