Subgroups — C₁₉×#18721 #18024680

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3544	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3248	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1646	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1645	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1644	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1643	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1483	C₂	1	2	yes	maximal, complemented
10	C₁₉×#563	—	2	2	no	—
11	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#555	C₂²	1	1	yes	characteristic
13	C₁₉×#554	C₂²	1	2	yes	—
14	C₁₉×#552	—	2	2	no	—
15	C₁₉×#547	—	2	2	no	—
16	C₁₉×#544	—	2	2	no	—
17	C₁₉×#542	—	2	2	no	—
18	C₁₉×#536	—	2	2	no	—
19	C₁₉×#533	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₉×#529	C₂²	1	2	yes	—
22	C₁₉×#491	—	2	2	no	—
23	C₁₉×#487	C₂²	1	2	yes	—
24	C₁₉×#487	C₂²	1	2	yes	—
25	C₁₉×#479	—	2	2	no	—
26	C₁₉×#475	C₂²	1	2	yes	—
27	C₁₉×#474	C₂²	1	2	yes	—
28	C₁₉×#467	—	2	2	no	—
29	C₁₉×#465	—	2	2	no	—
30	C₁₉×#464	—	2	2	no	—
31	C₁₉×#462	C₂²	1	2	yes	—
32	C₁₉×#461	C₂²	1	2	yes	—
33	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
34	C₁₉×#419	—	2	2	no	—
35	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#333	C₂²	1	1	yes	characteristic
37	C₁₉×#333	C₂²	1	1	yes	characteristic
38	C₁₉×#333	C₂²	1	2	yes	—
39	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
40	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
41	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
42	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
45	C₂×Q₁₆×C₁₉	—	2	2	no	—
46	C₂×SD₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	—	2	2	no	—
52	C₁₉×C₄⋊Q₈	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
54	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₁₉×#126	—	2	4	no	—
58	C₁₉×#126	—	2	2	no	—
59	C₁₉×#125	—	2	4	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₁₉×#125	—	2	1	no	—
62	C₁₉×#125	D₄	1	2	yes	—
63	C₁₉×#124	—	2	2	no	—
64	C₁₉×#124	—	2	2	no	—
65	C₁₉×#124	D₄	1	2	yes	—
66	C₁₉×#123	—	2	4	no	—
67	C₁₉×#123	—	2	4	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	4	no	—
70	C₁₉×C₂²⋊Q₈	—	2	4	no	—
71	C₁₉×C₂²⋊Q₈	—	2	4	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	D₄	1	2	yes	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	2	2	no	—
79	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	C₂³	1	2	yes	—
83	C₁₉×#117	—	2	2	no	—
84	C₁₉×#117	—	2	2	no	—
85	C₁₉×#117	—	2	2	no	—
86	C₁₉×#117	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×#107	—	2	2	no	—
91	C₁₉×#106	—	2	2	no	—
92	C₁₉×C₄⋊C₈	—	2	2	no	—
93	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
94	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
95	C₁₉×#103	—	2	4	no	—
96	C₁₉×#103	—	2	4	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#102	—	2	2	no	—
101	C₁₉×#97	—	2	1	no	—
102	C₄×C₈×C₁₉	C₂³	1	2	yes	—
103	#41×C₁₉	—	8	4	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	4	4	no	—
108	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
110	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	Q₁₆×C₁₉	—	8	2	no	—
120	SD₁₆×C₁₉	—	8	2	no	—
121	M₁₆×C₁₉	—	4	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	8	2	no	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	4	2	no	—
139	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₁₉	—	2	4	no	—
142	C₂²⋊C₄×C₁₉	—	2	4	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	2	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₉	—	4	1	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	4	1	no	—
153	C₄²×C₁₉	C₂×D₄	1	2	yes	—
154	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
156	#18721	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	#120	1	1	yes	characteristic
159	Q₈×C₁₉	—	2	2	no	—
160	Q₈×C₁₉	—	2	2	no	—
161	Q₈×C₁₉	—	4	2	no	—
162	Q₈×C₁₉	—	4	2	no	—
163	Q₈×C₁₉	—	4	2	no	—
164	Q₈×C₁₉	—	4	2	no	—
165	Q₈×C₁₉	—	8	2	no	—
166	Q₈×C₁₉	—	8	2	no	—
167	D₄×C₁₉	—	2	2	no	—
168	D₄×C₁₉	—	2	2	no	—
169	D₄×C₁₉	—	4	4	no	—
170	D₄×C₁₉	—	8	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	4	4	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	8	4	no	—
184	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#120	1	2	yes	—
186	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
188	C₈×C₁₉	—	4	2	no	—
189	C₈×C₁₉	—	4	2	no	—
190	C₈×C₁₉	—	4	2	no	—
191	#3544	C₂×C₁₉	1	1	yes	characteristic
192	#3248	C₂×C₁₉	1	2	yes	complemented
193	#3139	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#1646	C₂×C₁₉	1	2	yes	complemented
195	#1645	C₂×C₁₉	1	2	yes	complemented
196	#1644	C₂×C₁₉	1	2	yes	complemented
197	#1643	C₂×C₁₉	1	2	yes	complemented
198	C₂×#333	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#1483	C₂×C₁₉	1	2	yes	complemented
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	2	no	—
203	C₂²×C₁₉	—	4	2	no	—
204	C₂²×C₁₉	#455	1	2	yes	—
205	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	4	2	no	—
212	C₄×C₁₉	—	4	2	no	—
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	8	2	no	—
215	C₄×C₁₉	#577	1	2	yes	—
216	C₄×C₁₉	#578	1	2	yes	—
217	#563	—	2	2	no	—
218	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
219	#555	C₂²×C₁₉	1	1	yes	characteristic
220	#554	C₂²×C₁₉	1	2	yes	—
221	#552	—	2	2	no	—
222	#547	—	2	2	no	—
223	#544	—	2	2	no	—
224	#542	—	2	2	no	—
225	#536	—	2	2	no	—
226	#533	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
228	#529	C₂²×C₁₉	1	2	yes	—
229	#491	—	2	2	no	—
230	#487	C₂²×C₁₉	1	2	yes	—
231	#487	C₂²×C₁₉	1	2	yes	—
232	#479	—	2	2	no	—
233	#475	C₂²×C₁₉	1	2	yes	—
234	#474	C₂²×C₁₉	1	2	yes	—
235	#467	—	2	2	no	—
236	#465	—	2	2	no	—
237	#464	—	2	2	no	—
238	#462	C₂²×C₁₉	1	2	yes	—
239	#461	C₂²×C₁₉	1	2	yes	—
240	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
241	#419	—	2	2	no	—
242	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
243	#333	C₂²×C₁₉	1	1	yes	characteristic
244	#333	C₂²×C₁₉	1	1	yes	characteristic
245	#333	C₂²×C₁₉	1	2	yes	—
246	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
247	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
248	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
249	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
250	C₂×C₁₉	—	2	2	no	—
251	C₂×C₁₉	—	8	2	no	—
252	C₂×C₁₉	#3013	1	2	yes	—
253	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
254	C₂×#41	—	2	2	no	—
255	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×SD₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂²×C₈	—	2	2	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	—	2	2	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
265	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
266	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
267	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
268	#126	—	2	4	no	—
269	#126	—	2	2	no	—
270	#125	—	2	4	no	—
271	#125	—	2	2	no	—
272	#125	—	2	1	no	—
273	#125	D₄×C₁₉	1	2	yes	—
274	#124	—	2	2	no	—
275	#124	—	2	2	no	—
276	#124	D₄×C₁₉	1	2	yes	—
277	#123	—	2	4	no	—
278	#123	—	2	4	no	—
279	#123	—	2	2	no	—
280	C₂²⋊Q₈	—	2	4	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	—	2	2	no	—
284	C₂²⋊Q₈	—	2	2	no	—
285	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
286	#121	—	2	2	no	—
287	#121	D₄×C₁₉	1	2	yes	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	C₂³×C₁₉	1	2	yes	—
294	#117	—	2	2	no	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	#117	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
301	#107	—	2	2	no	—
302	#106	—	2	2	no	—
303	C₄⋊C₈	—	2	2	no	—
304	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
305	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
306	#103	—	2	4	no	—
307	#103	—	2	4	no	—
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#103	—	2	2	no	—
311	#102	—	2	2	no	—
312	#97	—	2	1	no	—
313	C₄×C₈	C₂³×C₁₉	1	2	yes	—
314	C₁₉	#18721	1	1	yes	characteristic, direct product factor, Sylow
315	#41	—	8	4	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
321	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
322	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
331	Q₁₆	—	8	2	no	—
332	SD₁₆	—	8	2	no	—
333	M₁₆	—	4	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	8	2	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
352	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
353	C₂²⋊C₄	—	2	4	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	4	1	no	—
365	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
366	C₄²	C₂×D₄×C₁₉	1	2	yes	—
367	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
368	C₂³	—	2	2	no	—
369	C₂³	C₁₉×#120	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	8	2	no	—
377	Q₈	—	8	2	no	—
378	D₄	—	2	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	4	no	—
381	D₄	—	8	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	4	no	—
395	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
396	C₂×C₄	C₁₉×#120	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	C₁₉×#455	1	2	yes	—
407	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	C₁₉×#577	1	2	yes	—
418	C₄	C₁₉×#578	1	2	yes	—
419	C₂	—	2	2	no	—
420	C₂	—	8	2	no	—
421	C₂	C₁₉×#3013	1	2	yes	—
422	C₂	C₂×C₁₉×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3544	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3248	C₂	semidirect
3. C₁₉×#3139	C₂	semidirect
4. C₁₉×#1646	C₂	semidirect
5. C₁₉×#1645	C₂	semidirect
6. C₁₉×#1644	C₂	semidirect
7. C₁₉×#1643	C₂	semidirect
8. C₂×C₁₉×#333	C₂	semidirect
9. C₁₉×#1483	C₂	semidirect
156. #18721	C₁₉	direct (N × H)
192. #3248	C₂×C₁₉	semidirect
193. #3139	C₂×C₁₉	semidirect
194. #1646	C₂×C₁₉	semidirect
195. #1645	C₂×C₁₉	semidirect
196. #1644	C₂×C₁₉	semidirect
197. #1643	C₂×C₁₉	semidirect
198. C₂×#333	C₂×C₁₉	semidirect
199. #1483	C₂×C₁₉	semidirect
314. C₁₉	#18721	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×#3544	2
C₁₉×#3248	2
C₁₉×#3139	2
C₁₉×#1646	2
C₁₉×#1645	2
C₁₉×#1644	2
C₁₉×#1643	2
C₂×C₁₉×#333	2
C₁₉×#1483	2
#18721	19

Subgroups — C19×#18721 #18024680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18721 #18024680