Subgroups — C₁₉×#11300 #18017259

Order 4864.

578 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#338	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#344	—	2	2	no	—
16	C₁₉×#344	—	2	2	no	—
17	C₁₉×#339	—	2	2	no	—
18	C₁₉×#339	—	2	2	no	—
19	C₁₉×#338	—	2	2	no	—
20	C₁₉×H(3,ℤ/4)	—	2	2	no	—
21	C₁₉×#336	C₄	1	4	yes	complemented
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×M₁₆×C₁₉	—	2	1	no	—
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₂×M₁₆×C₁₉	—	2	1	no	—
27	C₂×M₁₆×C₁₉	—	2	1	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	—	2	1	no	—
43	C₂×M₁₆×C₁₉	—	2	1	no	—
44	C₂×M₁₆×C₁₉	—	2	1	no	—
45	C₂×M₁₆×C₁₉	—	2	1	no	—
46	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
47	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
48	C₂²×C₈×C₁₉	—	2	1	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
52	C₁₉×#117	—	2	1	no	—
53	C₁₉×#117	—	2	1	no	—
54	C₁₉×#117	—	2	1	no	—
55	C₁₉×#117	—	2	1	no	—
56	C₁₉×#117	—	2	1	no	—
57	C₁₉×#117	—	2	1	no	—
58	C₁₉×#117	D₄	1	2	yes	—
59	C₁₉×#117	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
72	C₂⁴×C₁₉	#41	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	4	4	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	M₁₆×C₁₉	—	2	2	no	—
94	M₁₆×C₁₉	—	2	2	no	—
95	M₁₆×C₁₉	—	2	2	no	—
96	M₁₆×C₁₉	—	2	2	no	—
97	M₁₆×C₁₉	—	4	1	no	—
98	M₁₆×C₁₉	—	4	1	no	—
99	M₁₆×C₁₉	—	4	1	no	—
100	M₁₆×C₁₉	—	4	1	no	—
101	M₁₆×C₁₉	—	4	1	no	—
102	M₁₆×C₁₉	—	4	1	no	—
103	M₁₆×C₁₉	—	4	1	no	—
104	M₁₆×C₁₉	—	4	1	no	—
105	M₁₆×C₁₉	—	4	1	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	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	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	—	4	1	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	—	4	1	no	—
125	C₂²⋊C₄×C₁₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	—	2	2	no	—
131	C₄²×C₁₉	—	2	2	no	—
132	C₄²×C₁₉	—	2	2	no	—
133	C₄²×C₁₉	—	4	1	no	—
134	C₄²×C₁₉	—	4	1	no	—
135	C₄²×C₁₉	—	4	1	no	—
136	C₄²×C₁₉	—	4	1	no	—
137	#11300	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	#117	1	1	yes	characteristic
140	C₂³×C₁₉	#123	1	1	yes	characteristic
141	C₂³×C₁₉	#123	1	1	yes	characteristic
142	C₂³×C₁₉	#124	1	1	yes	characteristic
143	C₂³×C₁₉	#125	1	1	yes	characteristic
144	C₂³×C₁₉	#126	1	1	yes	characteristic
145	C₂³×C₁₉	#126	1	1	yes	characteristic
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	—	4	4	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	8	2	no	—
154	C₂×C₄×C₁₉	—	8	2	no	—
155	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
183	C₈×C₁₉	—	4	2	no	—
184	C₈×C₁₉	—	4	2	no	—
185	C₈×C₁₉	—	4	2	no	—
186	C₈×C₁₉	—	4	2	no	—
187	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
188	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
189	C₂×#339	C₂×C₁₉	1	1	yes	characteristic
190	C₂×#339	C₂×C₁₉	1	1	yes	characteristic
191	C₂×#338	C₂×C₁₉	1	1	yes	characteristic
192	C₂×H(3,ℤ/4)	C₂×C₁₉	1	1	yes	characteristic
193	#1728	C₂×C₁₉	1	1	yes	characteristic
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	4	1	no	—
201	C₂²×C₁₉	#383	1	1	yes	characteristic
202	C₂²×C₁₉	#387	1	1	yes	characteristic
203	C₂²×C₁₉	#388	1	1	yes	characteristic
204	C₂²×C₁₉	#397	1	1	yes	characteristic
205	C₂²×C₁₉	#397	1	1	yes	characteristic
206	C₂²×C₁₉	#400	1	1	yes	characteristic
207	C₂²×C₁₉	#400	1	1	yes	characteristic
208	C₄×C₁₉	—	4	4	no	—
209	C₄×C₁₉	—	8	2	no	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	#387	1	1	yes	characteristic
212	C₄×C₁₉	#387	1	1	yes	characteristic
213	C₄×C₁₉	#388	1	1	yes	characteristic
214	C₄×C₁₉	#388	1	1	yes	characteristic
215	C₄×C₁₉	#396	1	1	yes	characteristic
216	C₄×C₁₉	#397	1	1	yes	characteristic
217	C₄×C₁₉	#400	1	1	yes	characteristic
218	C₄×C₁₉	#401	1	1	yes	characteristic
219	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
220	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
221	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
222	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
225	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
226	#344	—	2	2	no	—
227	#344	—	2	2	no	—
228	#339	—	2	2	no	—
229	#339	—	2	2	no	—
230	#338	—	2	2	no	—
231	H(3,ℤ/4)	—	2	2	no	—
232	#336	C₄×C₁₉	1	4	yes	complemented
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	2	1	no	—
235	C₂×C₁₉	—	2	1	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	#1443	1	1	yes	characteristic
240	C₂×C₁₉	#1841	1	2	yes	—
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
266	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
270	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
271	#117	—	2	1	no	—
272	#117	—	2	1	no	—
273	#117	—	2	1	no	—
274	#117	—	2	1	no	—
275	#117	—	2	1	no	—
276	#117	—	2	1	no	—
277	#117	D₄×C₁₉	1	2	yes	—
278	#117	D₄×C₁₉	1	2	yes	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
291	C₁₉	#11300	1	1	yes	characteristic, direct product factor, Sylow
292	C₂⁴	#41×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
304	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
309	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
311	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
313	M₁₆	—	2	2	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	4	1	no	—
319	M₁₆	—	4	1	no	—
320	M₁₆	—	4	1	no	—
321	M₁₆	—	4	1	no	—
322	M₁₆	—	4	1	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	4	1	no	—
327	M₁₆	—	4	1	no	—
328	M₁₆	—	4	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	4	1	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	C₁₉×#117	1	1	yes	characteristic
359	C₂³	C₁₉×#123	1	1	yes	characteristic
360	C₂³	C₁₉×#123	1	1	yes	characteristic
361	C₂³	C₁₉×#124	1	1	yes	characteristic
362	C₂³	C₁₉×#125	1	1	yes	characteristic
363	C₂³	C₁₉×#126	1	1	yes	characteristic
364	C₂³	C₁₉×#126	1	1	yes	characteristic
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
375	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
376	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
377	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
378	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
379	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
380	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
381	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
382	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
383	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
384	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
385	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
386	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
387	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
388	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
389	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
390	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
391	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
392	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
393	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
394	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
395	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
396	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
397	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
398	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
399	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
400	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
401	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
402	C₈	—	4	2	no	—
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	C₁₉×#383	1	1	yes	characteristic
414	C₂²	C₁₉×#387	1	1	yes	characteristic
415	C₂²	C₁₉×#388	1	1	yes	characteristic
416	C₂²	C₁₉×#397	1	1	yes	characteristic
417	C₂²	C₁₉×#397	1	1	yes	characteristic
418	C₂²	C₁₉×#400	1	1	yes	characteristic
419	C₂²	C₁₉×#400	1	1	yes	characteristic
420	C₄	—	4	4	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₁₉×#387	1	1	yes	characteristic
424	C₄	C₁₉×#387	1	1	yes	characteristic
425	C₄	C₁₉×#388	1	1	yes	characteristic
426	C₄	C₁₉×#388	1	1	yes	characteristic
427	C₄	C₁₉×#396	1	1	yes	characteristic
428	C₄	C₁₉×#397	1	1	yes	characteristic
429	C₄	C₁₉×#400	1	1	yes	characteristic
430	C₄	C₁₉×#401	1	1	yes	characteristic
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	C₁₉×#1443	1	1	yes	characteristic
438	C₂	C₁₉×#1841	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#117
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#383
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×M₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
21. C₁₉×#336	C₄	semidirect
137. #11300	C₁₉	direct (N × H)
232. #336	C₄×C₁₉	semidirect
291. C₁₉	#11300	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#344	2
C₂×C₁₉×#339	2
C₂×C₁₉×#338	2
C₂×C₁₉×H(3,ℤ/4)	2
C₁₉×#1728	2
#11300	19

Subgroups — C19×#11300 #18017259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11300 #18017259