Subgroups — C₁₉×#32940 #18038899

Order 4864.

1378 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#470	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2616	C₂	1	2	yes	maximal
5	C₁₉×#1894	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1892	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1809	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#131	—	2	8	no	—
12	C₂×C₁₉×#131	—	2	4	no	—
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₁₉×#470	—	2	8	no	—
20	C₁₉×#467	—	2	4	no	—
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	4	yes	—
25	C₁₉×#395	—	2	2	no	—
26	C₁₉×#394	—	2	2	no	—
27	C₁₉×#394	—	2	4	no	—
28	C₁₉×#380	C₂²	1	4	yes	—
29	C₁₉×#380	C₂²	1	2	yes	—
30	C₁₉×#340	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	4	yes	—
32	C₂×#41×C₁₉	—	2	4	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
37	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
38	C₂²×D₄×C₁₉	D₄	1	2	yes	—
39	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×Q₁₆×C₁₉	—	2	2	no	—
43	C₂×Q₁₆×C₁₉	—	2	4	no	—
44	C₁₉×#131	—	2	32	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	2	4	no	—
47	C₂×M₁₆×C₁₉	—	2	4	no	—
48	C₂×M₁₆×C₁₉	—	2	4	no	—
49	C₂×M₁₆×C₁₉	D₄	1	8	yes	—
50	C₂²×C₈×C₁₉	—	2	4	no	—
51	C₂²×C₈×C₁₉	—	2	4	no	—
52	C₂²×C₈×C₁₉	—	2	4	no	—
53	C₂²×C₈×C₁₉	—	2	4	no	—
54	C₂²×C₈×C₁₉	D₄	1	4	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	8	no	—
60	C₁₉×C₂²⋊Q₈	—	2	8	no	—
61	C₁₉×C₂²⋊Q₈	—	2	4	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₁₉×#107	—	2	2	no	—
71	C₁₉×#106	—	2	4	no	—
72	C₁₉×#103	—	2	4	no	—
73	C₁₉×#103	—	2	8	no	—
74	C₁₉×#95	—	2	4	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
77	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
78	#41×C₁₉	—	2	8	no	—
79	#41×C₁₉	—	2	16	no	—
80	#41×C₁₉	—	2	8	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	2	4	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	4	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	#41	1	2	yes	—
106	C₂²×C₄×C₁₉	#41	1	4	yes	—
107	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
108	Q₁₆×C₁₉	—	4	4	no	—
109	M₁₆×C₁₉	—	2	8	no	—
110	M₁₆×C₁₉	—	2	16	no	—
111	C₂×C₈×C₁₉	—	2	16	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	8	no	—
116	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
118	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
119	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
120	C₄⋊C₄×C₁₉	—	2	4	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	4	4	no	—
125	C₄⋊C₄×C₁₉	—	4	8	no	—
126	C₂²⋊C₄×C₁₉	—	4	4	no	—
127	C₂²⋊C₄×C₁₉	—	4	8	no	—
128	C₂²⋊C₄×C₁₉	—	8	4	no	—
129	C₂²⋊C₄×C₁₉	—	8	2	no	—
130	#32940	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	4	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	4	no	—
138	C₂³×C₁₉	#121	1	2	yes	—
139	C₂³×C₁₉	#121	1	4	yes	—
140	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₉	—	2	8	no	—
142	Q₈×C₁₉	—	4	2	no	—
143	Q₈×C₁₉	—	4	2	no	—
144	Q₈×C₁₉	—	4	4	no	—
145	D₄×C₁₉	—	2	16	no	—
146	D₄×C₁₉	—	2	8	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	2	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	4	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	#121	1	2	yes	—
166	C₂×C₄×C₁₉	#121	1	4	yes	—
167	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
171	C₈×C₁₉	—	2	2	no	—
172	C₈×C₁₉	—	2	4	no	—
173	C₈×C₁₉	#120	1	4	yes	—
174	C₂²×#131	C₂×C₁₉	1	1	yes	characteristic
175	C₂×#470	C₂×C₁₉	1	2	yes	complemented
176	C₂×#467	C₂×C₁₉	1	1	yes	characteristic, complemented
177	#2616	C₂×C₁₉	1	2	yes	—
178	#1894	C₂×C₁₉	1	2	yes	complemented
179	#1892	C₂×C₁₉	1	4	yes	complemented
180	#1809	C₂×C₁₉	1	2	yes	complemented
181	#1807	C₂×C₁₉	1	1	yes	characteristic, complemented
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	8	no	—
187	C₂²×C₁₉	—	4	2	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	4	no	—
190	C₂²×C₁₉	—	4	4	no	—
191	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#121	1	2	yes	—
193	C₂²×C₁₉	#577	1	2	yes	—
194	C₂²×C₁₉	#578	1	2	yes	—
195	C₄×C₁₉	—	2	4	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	8	2	no	—
198	C₄×C₁₉	—	8	2	no	—
199	C₄×C₁₉	—	8	4	no	—
200	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
201	C₄×C₁₉	#525	1	2	yes	—
202	C₄×C₁₉	#525	1	1	yes	characteristic
203	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
205	C₂×#131	—	2	8	no	—
206	C₂×#131	—	2	4	no	—
207	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
209	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
210	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
212	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
213	#470	—	2	8	no	—
214	#467	—	2	4	no	—
215	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×#106	C₂²×C₁₉	1	2	yes	—
217	C₂×#103	C₂²×C₁₉	1	2	yes	—
218	C₂×#103	C₂²×C₁₉	1	4	yes	—
219	#395	—	2	2	no	—
220	#394	—	2	2	no	—
221	#394	—	2	4	no	—
222	#380	C₂²×C₁₉	1	2	yes	—
223	#380	C₂²×C₁₉	1	4	yes	—
224	#340	C₂²×C₁₉	1	2	yes	—
225	#340	C₂²×C₁₉	1	4	yes	—
226	C₂×C₁₉	—	4	2	no	—
227	C₂×C₁₉	—	4	4	no	—
228	C₂×C₁₉	#2847	1	1	yes	characteristic
229	C₂×C₁₉	#3059	1	1	yes	characteristic
230	C₂×C₁₉	#3060	1	1	yes	characteristic
231	C₂×C₁₉	#3063	1	4	yes	—
232	C₂×#41	—	2	4	no	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	4	no	—
236	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
237	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
238	C₂²×D₄	D₄×C₁₉	1	2	yes	—
239	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
241	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
242	C₂×Q₁₆	—	2	2	no	—
243	C₂×Q₁₆	—	2	4	no	—
244	#131	—	2	32	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	D₄×C₁₉	1	8	yes	—
250	C₂²×C₈	—	2	4	no	—
251	C₂²×C₈	—	2	4	no	—
252	C₂²×C₈	—	2	4	no	—
253	C₂²×C₈	—	2	4	no	—
254	C₂²×C₈	D₄×C₁₉	1	4	yes	—
255	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
257	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
258	C₂²⋊Q₈	—	2	4	no	—
259	C₂²⋊Q₈	—	2	8	no	—
260	C₂²⋊Q₈	—	2	8	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	4	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	4	no	—
270	#107	—	2	2	no	—
271	#106	—	2	4	no	—
272	#103	—	2	4	no	—
273	#103	—	2	8	no	—
274	#95	—	2	2	no	—
275	#95	—	2	4	no	—
276	C₁₉	#32940	1	1	yes	characteristic, direct product factor, Sylow
277	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
278	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
279	#41	—	2	8	no	—
280	#41	—	2	16	no	—
281	#41	—	2	8	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
305	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
306	C₂²×C₄	#41×C₁₉	1	2	yes	—
307	C₂²×C₄	#41×C₁₉	1	4	yes	—
308	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
309	Q₁₆	—	4	4	no	—
310	M₁₆	—	2	8	no	—
311	M₁₆	—	2	16	no	—
312	C₂×C₈	—	2	16	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	8	no	—
317	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
318	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
319	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
320	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	8	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	4	8	no	—
329	C₂²⋊C₄	—	8	4	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	C₁₉×#121	1	2	yes	—
339	C₂³	C₁₉×#121	1	4	yes	—
340	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
341	Q₈	—	2	8	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	4	no	—
345	D₄	—	2	16	no	—
346	D₄	—	2	8	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	C₁₉×#121	1	2	yes	—
366	C₂×C₄	C₁₉×#121	1	4	yes	—
367	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
369	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
370	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
371	C₈	—	2	2	no	—
372	C₈	—	2	4	no	—
373	C₈	C₁₉×#120	1	4	yes	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	8	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
384	C₂²	C₂×C₁₉×#121	1	2	yes	—
385	C₂²	C₁₉×#577	1	2	yes	—
386	C₂²	C₁₉×#578	1	2	yes	—
387	C₄	—	2	4	no	—
388	C₄	—	2	2	no	—
389	C₄	—	8	2	no	—
390	C₄	—	8	4	no	—
391	C₄	—	8	2	no	—
392	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
393	C₄	C₁₉×#525	1	2	yes	—
394	C₄	C₁₉×#525	1	1	yes	characteristic
395	C₂	—	4	2	no	—
396	C₂	—	4	4	no	—
397	C₂	C₁₉×#2847	1	1	yes	characteristic
398	C₂	C₁₉×#3059	1	1	yes	characteristic
399	C₂	C₁₉×#3060	1	1	yes	characteristic
400	C₂	C₁₉×#3063	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#470	C₂	semidirect
3. C₂×C₁₉×#467	C₂	semidirect
5. C₁₉×#1894	C₂	semidirect
6. C₁₉×#1892	C₂	semidirect
7. C₁₉×#1809	C₂	semidirect
8. C₁₉×#1807	C₂	semidirect
130. #32940	C₁₉	direct (N × H)
175. C₂×#470	C₂×C₁₉	semidirect
176. C₂×#467	C₂×C₁₉	semidirect
178. #1894	C₂×C₁₉	semidirect
179. #1892	C₂×C₁₉	semidirect
180. #1809	C₂×C₁₉	semidirect
181. #1807	C₂×C₁₉	semidirect
276. C₁₉	#32940	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×#131	2
C₂×C₁₉×#470	2
C₂×C₁₉×#467	2
C₁₉×#2616	2
C₁₉×#1894	2
C₁₉×#1892	2
C₁₉×#1809	2
C₁₉×#1807	2
#32940	19

Subgroups — C19×#32940 #18038899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32940 #18038899