Subgroups — C₁₉×#21858 #18027817

Order 4864.

1038 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3455	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2905	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1994	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1963	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1871	C₂	1	4	yes	maximal, complemented
9	C₁₉×#1806	C₂	1	4	yes	maximal, complemented
10	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#542	C₄	1	4	yes	complemented
12	C₁₉×#541	C₄	1	2	yes	complemented
13	C₁₉×#540	C₄	1	2	yes	complemented
14	C₁₉×#539	—	2	2	no	—
15	C₁₉×#538	—	2	2	no	—
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₁₉×#529	—	2	4	no	—
19	C₁₉×#525	C₂²	1	2	yes	—
20	C₄×#41×C₁₉	C₂²	1	2	yes	—
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₁₉×#424	—	2	4	no	—
23	C₁₉×#423	C₂²	1	1	yes	characteristic
24	C₁₉×#423	C₂²	1	1	yes	characteristic
25	C₁₉×#423	C₂²	1	2	yes	—
26	C₂×C₁₉×#104	C₂²	1	4	yes	—
27	C₂×C₁₉×#104	C₂²	1	4	yes	—
28	C₁₉×#388	—	2	2	no	—
29	C₁₉×#387	—	2	2	no	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
32	C₁₉×#376	C₂²	1	1	yes	characteristic
33	C₄³×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#339	C₂²	1	4	yes	—
35	C₁₉×#339	C₂²	1	4	yes	—
36	C₂×#41×C₁₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₁₉	—	2	2	no	—
39	C₂×M₁₆×C₁₉	—	4	4	no	—
40	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
41	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₉	—	2	2	no	—
43	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
44	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
45	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
46	C₁₉×#126	—	2	4	no	—
47	C₁₉×#126	—	2	4	no	—
48	C₁₉×#125	—	2	4	no	—
49	C₁₉×#125	C₂×C₄	1	2	yes	—
50	C₁₉×#124	—	2	4	no	—
51	C₁₉×#124	C₂×C₄	1	2	yes	—
52	C₁₉×#123	—	2	2	no	—
53	C₁₉×#123	—	2	4	no	—
54	C₁₉×#123	—	2	4	no	—
55	C₁₉×C₂²⋊Q₈	—	2	2	no	—
56	C₁₉×C₂²⋊Q₈	—	2	4	no	—
57	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
58	C₁₉×#121	—	2	2	no	—
59	C₁₉×#121	—	2	4	no	—
60	C₁₉×#121	C₂×C₄	1	4	yes	—
61	C₁₉×#120	—	2	2	no	—
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
64	C₄×D₄×C₁₉	—	2	4	no	—
65	C₄×D₄×C₁₉	—	2	4	no	—
66	C₄×D₄×C₁₉	—	2	2	no	—
67	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
68	C₁₉×#117	—	2	2	no	—
69	C₁₉×#117	C₂×C₄	1	2	yes	—
70	C₁₉×#117	C₂×C₄	1	2	yes	—
71	C₁₉×#117	D₄	1	4	yes	—
72	C₁₉×#117	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
77	C₂×C₄²×C₁₉	—	2	2	no	—
78	C₂×C₄²×C₁₉	—	2	2	no	—
79	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
80	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	—	2	4	no	—
84	C₁₉×C₄⋊C₈	—	2	2	no	—
85	C₁₉×C₄⋊C₈	—	2	2	no	—
86	C₁₉×#104	—	4	4	no	—
87	C₁₉×#104	—	4	4	no	—
88	C₁₉×#95	—	2	2	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
92	#41×C₁₉	—	2	4	no	—
93	#41×C₁₉	—	2	4	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	4	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₁₉	—	2	4	no	—
113	M₁₆×C₁₉	—	2	4	no	—
114	M₁₆×C₁₉	—	4	4	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	4	4	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	4	no	—
121	C₄⋊C₄×C₁₉	—	2	4	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	4	4	no	—
124	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
125	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
126	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
127	C₂²⋊C₄×C₁₉	—	2	4	no	—
128	C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂²⋊C₄×C₁₉	—	2	4	no	—
130	C₂²⋊C₄×C₁₉	—	2	4	no	—
131	C₂²⋊C₄×C₁₉	—	2	4	no	—
132	C₂²⋊C₄×C₁₉	—	4	4	no	—
133	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
134	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
135	C₄²×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	2	2	no	—
140	C₄²×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	4	4	no	—
142	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
143	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₁₉	C₂×D₄	1	2	yes	—
146	C₄²×C₁₉	C₂×D₄	1	2	yes	—
147	#21858	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	4	2	no	—
151	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₁₉	—	2	4	no	—
154	Q₈×C₁₉	—	8	2	no	—
155	D₄×C₁₉	—	2	4	no	—
156	D₄×C₁₉	—	4	4	no	—
157	D₄×C₁₉	—	8	2	no	—
158	D₄×C₁₉	—	8	4	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	8	4	no	—
176	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
183	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
184	C₈×C₁₉	—	4	2	no	—
185	C₈×C₁₉	—	4	2	no	—
186	#3455	C₂×C₁₉	1	1	yes	characteristic
187	#2905	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#2298	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1995	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1994	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1963	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#1962	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#1871	C₂×C₁₉	1	4	yes	complemented
194	#1806	C₂×C₁₉	1	4	yes	complemented
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	4	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	—	4	4	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
202	C₂²×C₁₉	#537	1	2	yes	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	4	no	—
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	4	4	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	4	4	no	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	#520	1	2	yes	—
212	C₄×C₁₉	#535	1	1	yes	characteristic
213	C₄×C₁₉	#536	1	1	yes	characteristic
214	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
215	#542	C₄×C₁₉	1	4	yes	complemented
216	#541	C₄×C₁₉	1	2	yes	complemented
217	#540	C₄×C₁₉	1	2	yes	complemented
218	#539	—	2	2	no	—
219	#538	—	2	2	no	—
220	#533	C₂²×C₁₉	1	1	yes	characteristic
221	#532	C₂²×C₁₉	1	1	yes	characteristic
222	#529	—	2	4	no	—
223	#525	C₂²×C₁₉	1	2	yes	—
224	C₄×#41	C₂²×C₁₉	1	2	yes	—
225	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
226	#424	—	2	4	no	—
227	#423	C₂²×C₁₉	1	2	yes	—
228	#423	C₂²×C₁₉	1	1	yes	characteristic
229	#423	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#104	C₂²×C₁₉	1	4	yes	—
231	C₂×#104	C₂²×C₁₉	1	4	yes	—
232	#388	—	2	2	no	—
233	#387	—	2	2	no	—
234	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
235	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
236	#376	C₂²×C₁₉	1	1	yes	characteristic
237	C₄³	C₂²×C₁₉	1	1	yes	characteristic
238	#339	C₂²×C₁₉	1	4	yes	—
239	#339	C₂²×C₁₉	1	4	yes	—
240	C₂×C₁₉	—	2	2	no	—
241	C₂×C₁₉	—	4	2	no	—
242	C₂×C₁₉	—	8	2	no	—
243	C₂×C₁₉	#2311	1	1	yes	characteristic
244	C₂×C₁₉	#2901	1	2	yes	—
245	C₂×#41	C₂³×C₁₉	1	2	yes	—
246	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	4	4	no	—
249	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
250	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
251	C₂²×C₈	—	2	2	no	—
252	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
253	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
254	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
255	#126	—	2	4	no	—
256	#126	—	2	4	no	—
257	#125	—	2	4	no	—
258	#125	C₂×C₄×C₁₉	1	2	yes	—
259	#124	—	2	4	no	—
260	#124	C₂×C₄×C₁₉	1	2	yes	—
261	#123	—	2	2	no	—
262	#123	—	2	4	no	—
263	#123	—	2	4	no	—
264	C₂²⋊Q₈	—	2	2	no	—
265	C₂²⋊Q₈	—	2	4	no	—
266	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
267	#121	—	2	2	no	—
268	#121	—	2	4	no	—
269	#121	C₂×C₄×C₁₉	1	4	yes	—
270	#120	—	2	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
277	#117	—	2	2	no	—
278	#117	C₂×C₄×C₁₉	1	2	yes	—
279	#117	C₂×C₄×C₁₉	1	2	yes	—
280	#117	D₄×C₁₉	1	4	yes	—
281	#117	C₂³×C₁₉	1	2	yes	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
289	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
292	C₄⋊C₈	—	2	4	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	#104	—	4	4	no	—
296	#104	—	4	4	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	C₁₉	#21858	1	1	yes	characteristic, direct product factor, Sylow
301	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
322	M₁₆	—	2	4	no	—
323	M₁₆	—	2	4	no	—
324	M₁₆	—	4	4	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	4	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
335	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
336	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
344	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	4	4	no	—
352	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
353	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
354	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
355	C₄²	C₂×D₄×C₁₉	1	2	yes	—
356	C₄²	C₂×D₄×C₁₉	1	2	yes	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
361	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
362	Q₈	—	2	4	no	—
363	Q₈	—	8	2	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	8	2	no	—
367	D₄	—	8	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	4	no	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
386	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
388	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
389	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
391	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
392	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	8	2	no	—
401	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
402	C₂²	C₁₉×#537	1	2	yes	—
403	C₄	—	2	2	no	—
404	C₄	—	2	4	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	8	2	no	—
411	C₄	C₁₉×#520	1	2	yes	—
412	C₄	C₁₉×#535	1	1	yes	characteristic
413	C₄	C₁₉×#536	1	1	yes	characteristic
414	C₂	—	2	2	no	—
415	C₂	—	4	2	no	—
416	C₂	—	8	2	no	—
417	C₂	C₁₉×#2311	1	1	yes	characteristic
418	C₂	C₁₉×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₁₉×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2905	C₂	semidirect
3. C₁₉×#2298	C₂	semidirect
4. C₁₉×#1995	C₂	semidirect
5. C₁₉×#1994	C₂	semidirect
6. C₁₉×#1963	C₂	semidirect
7. C₁₉×#1962	C₂	semidirect
8. C₁₉×#1871	C₂	semidirect
9. C₁₉×#1806	C₂	semidirect
11. C₁₉×#542	C₄	semidirect
12. C₁₉×#541	C₄	semidirect
13. C₁₉×#540	C₄	semidirect
147. #21858	C₁₉	direct (N × H)
187. #2905	C₂×C₁₉	semidirect
188. #2298	C₂×C₁₉	semidirect
189. #1995	C₂×C₁₉	semidirect
190. #1994	C₂×C₁₉	semidirect
191. #1963	C₂×C₁₉	semidirect
192. #1962	C₂×C₁₉	semidirect
193. #1871	C₂×C₁₉	semidirect
194. #1806	C₂×C₁₉	semidirect
215. #542	C₄×C₁₉	semidirect
216. #541	C₄×C₁₉	semidirect
217. #540	C₄×C₁₉	semidirect
300. C₁₉	#21858	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×#3455	2
C₁₉×#2905	2
C₁₉×#2298	2
C₁₉×#1995	2
C₁₉×#1994	2
C₁₉×#1963	2
C₁₉×#1962	2
C₁₉×#1871	2
C₁₉×#1806	2
#21858	19

Subgroups — C19×#21858 #18027817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21858 #18027817