Subgroups — C₁₉×#23603 #18029562

Order 4864.

970 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#430	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2911	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2905	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2064	C₂	1	8	yes	maximal, complemented
8	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×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	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₁₉×#430	—	2	4	no	—
17	C₂×C₁₉×#108	C₂²	1	4	yes	—
18	C₁₉×#428	—	2	2	no	—
19	C₁₉×#428	C₂²	1	4	yes	—
20	C₁₉×#427	—	2	2	no	—
21	C₁₉×#424	—	2	2	no	—
22	C₁₉×#424	C₂²	1	4	yes	—
23	C₁₉×#423	—	2	2	no	—
24	C₁₉×#419	—	2	2	no	—
25	C₁₉×#419	—	2	2	no	—
26	C₁₉×#419	—	2	2	no	—
27	C₁₉×#419	C₂²	1	4	yes	—
28	C₂×C₁₉×#103	—	2	2	no	—
29	C₂×C₁₉×#103	C₂²	1	4	yes	—
30	C₂×C₁₉×#101	—	2	4	no	—
31	C₂×C₁₉×#101	C₂²	1	4	yes	—
32	C₁₉×#343	C₂²	1	4	yes	—
33	C₂²×Q₈×C₁₉	—	2	2	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	2	no	—
40	C₂²×Q₈×C₁₉	—	2	2	no	—
41	C₂²×Q₈×C₁₉	Q₈	1	4	yes	—
42	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	—	2	1	no	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₁₉	—	2	1	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	—	2	2	no	—
55	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
56	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
57	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
58	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
59	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
60	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	—	2	1	no	—
67	C₁₉×#117	—	2	1	no	—
68	C₁₉×#117	—	2	1	no	—
69	C₁₉×#117	—	2	1	no	—
70	C₁₉×#117	—	2	1	no	—
71	C₁₉×#117	D₄	1	2	yes	—
72	C₁₉×#117	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₁₉×#108	—	2	8	no	—
80	C₁₉×#107	—	2	4	no	—
81	C₁₉×#106	—	2	4	no	—
82	C₁₉×C₄⋊C₈	—	2	8	no	—
83	C₁₉×#103	—	2	8	no	—
84	C₁₉×#103	—	2	8	no	—
85	C₁₉×#101	—	2	8	no	—
86	C₂⁴×C₁₉	#41	1	1	yes	characteristic
87	C₂×Q₈×C₁₉	—	2	4	no	—
88	C₂×Q₈×C₁₉	—	2	2	no	—
89	C₂×Q₈×C₁₉	—	2	4	no	—
90	C₂×Q₈×C₁₉	—	2	4	no	—
91	C₂×Q₈×C₁₉	—	2	4	no	—
92	C₂×Q₈×C₁₉	—	2	4	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	4	1	no	—
98	C₂×Q₈×C₁₉	—	4	1	no	—
99	C₂×Q₈×C₁₉	—	4	2	no	—
100	C₂×Q₈×C₁₉	—	4	2	no	—
101	C₂×Q₈×C₁₉	—	4	2	no	—
102	C₂×Q₈×C₁₉	—	4	2	no	—
103	C₂×Q₈×C₁₉	—	4	2	no	—
104	C₂×Q₈×C₁₉	C₂×Q₈	1	4	yes	—
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	#41	1	2	yes	—
120	C₂²×C₄×C₁₉	#41	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	M₁₆×C₁₉	—	2	4	no	—
123	M₁₆×C₁₉	—	2	4	no	—
124	M₁₆×C₁₉	—	2	4	no	—
125	M₁₆×C₁₉	—	2	2	no	—
126	M₁₆×C₁₉	—	2	2	no	—
127	M₁₆×C₁₉	—	2	2	no	—
128	M₁₆×C₁₉	—	2	2	no	—
129	M₁₆×C₁₉	—	2	2	no	—
130	M₁₆×C₁₉	—	4	2	no	—
131	M₁₆×C₁₉	—	4	2	no	—
132	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
133	C₂×C₈×C₁₉	—	2	4	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	4	2	no	—
140	C₂×C₈×C₁₉	—	4	2	no	—
141	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₉	—	4	1	no	—
149	C₂²⋊C₄×C₁₉	—	4	1	no	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	4	1	no	—
153	C₄²×C₁₉	—	4	1	no	—
154	#23603	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	#121	1	1	yes	characteristic
157	C₂³×C₁₉	#121	1	1	yes	characteristic
158	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
159	C₂³×C₁₉	#126	1	2	yes	—
160	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
161	Q₈×C₁₉	—	2	4	no	—
162	Q₈×C₁₉	—	2	4	no	—
163	Q₈×C₁₉	—	4	2	no	—
164	Q₈×C₁₉	—	4	2	no	—
165	Q₈×C₁₉	—	4	4	no	—
166	Q₈×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	4	no	—
172	C₂×C₄×C₁₉	—	4	4	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	8	2	no	—
175	C₂×C₄×C₁₉	—	8	2	no	—
176	C₂×C₄×C₁₉	#121	1	2	yes	—
177	C₂×C₄×C₁₉	#121	1	2	yes	—
178	C₂×C₄×C₁₉	#121	1	2	yes	—
179	C₂×C₄×C₁₉	#121	1	2	yes	—
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
183	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
185	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
186	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
187	C₂×C₄×C₁₉	#126	1	2	yes	—
188	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
194	C₈×C₁₉	—	2	4	no	—
195	C₈×C₁₉	—	2	4	no	—
196	C₈×C₁₉	—	4	2	no	—
197	C₈×C₁₉	—	4	2	no	—
198	C₂×#430	C₂×C₁₉	1	1	yes	characteristic
199	#2911	C₂×C₁₉	1	1	yes	characteristic
200	#2905	C₂×C₁₉	1	1	yes	characteristic
201	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
202	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
203	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic
204	#2064	C₂×C₁₉	1	8	yes	complemented
205	#1742	C₂×C₁₉	1	1	yes	characteristic
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	#396	1	2	yes	—
212	C₂²×C₁₉	#396	1	2	yes	—
213	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
214	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#126	1	1	yes	characteristic
216	C₄×C₁₉	—	4	4	no	—
217	C₄×C₁₉	—	4	4	no	—
218	C₄×C₁₉	—	8	2	no	—
219	C₄×C₁₉	#396	1	2	yes	—
220	C₄×C₁₉	#396	1	2	yes	—
221	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
222	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
223	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
224	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
225	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
226	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
228	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
229	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
231	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
232	#430	—	2	4	no	—
233	C₂×#108	C₂²×C₁₉	1	4	yes	—
234	#428	—	2	2	no	—
235	#428	C₂²×C₁₉	1	4	yes	—
236	#427	—	2	2	no	—
237	#424	—	2	2	no	—
238	#424	C₂²×C₁₉	1	4	yes	—
239	#423	—	2	2	no	—
240	#419	—	2	2	no	—
241	#419	—	2	2	no	—
242	#419	—	2	2	no	—
243	#419	C₂²×C₁₉	1	4	yes	—
244	C₂×#103	—	2	2	no	—
245	C₂×#103	C₂²×C₁₉	1	4	yes	—
246	C₂×#101	—	2	4	no	—
247	C₂×#101	C₂²×C₁₉	1	4	yes	—
248	#343	C₂²×C₁₉	1	4	yes	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	2	1	no	—
251	C₂×C₁₉	—	2	2	no	—
252	C₂×C₁₉	—	2	2	no	—
253	C₂×C₁₉	C₂×#396	1	1	yes	characteristic
254	C₂×C₁₉	#3069	1	2	yes	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂²×Q₈	—	2	2	no	—
262	C₂²×Q₈	—	2	2	no	—
263	C₂²×Q₈	Q₈×C₁₉	1	4	yes	—
264	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
278	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
279	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
280	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
281	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
282	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
287	#117	—	2	1	no	—
288	#117	—	2	1	no	—
289	#117	—	2	1	no	—
290	#117	—	2	1	no	—
291	#117	—	2	1	no	—
292	#117	—	2	1	no	—
293	#117	D₄×C₁₉	1	2	yes	—
294	#117	C₂³×C₁₉	1	2	yes	—
295	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	#108	—	2	8	no	—
302	#107	—	2	4	no	—
303	#106	—	2	4	no	—
304	C₄⋊C₈	—	2	8	no	—
305	#103	—	2	8	no	—
306	#103	—	2	8	no	—
307	#101	—	2	8	no	—
308	C₁₉	#23603	1	1	yes	characteristic, direct product factor, Sylow
309	C₂⁴	#41×C₁₉	1	1	yes	characteristic
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	C₂×Q₈×C₁₉	1	4	yes	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
341	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	#41×C₁₉	1	2	yes	—
343	C₂²×C₄	#41×C₁₉	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	4	no	—
347	M₁₆	—	2	4	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	4	2	no	—
354	M₁₆	—	4	2	no	—
355	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	4	1	no	—
376	C₄²	—	4	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	C₁₉×#121	1	1	yes	characteristic
379	C₂³	C₁₉×#121	1	1	yes	characteristic
380	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
381	C₂³	C₁₉×#126	1	2	yes	—
382	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	Q₈	—	2	4	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	4	4	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
399	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
400	C₂×C₄	C₁₉×#121	1	2	yes	—
401	C₂×C₄	C₁₉×#121	1	2	yes	—
402	C₂×C₄	C₁₉×#121	1	2	yes	—
403	C₂×C₄	C₁₉×#121	1	2	yes	—
404	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
405	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
406	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
407	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
408	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
409	C₂×C₄	C₁₉×#126	1	2	yes	—
410	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
416	C₈	—	2	4	no	—
417	C₈	—	2	4	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	C₁₉×#396	1	2	yes	—
426	C₂²	C₁₉×#396	1	2	yes	—
427	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
428	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
429	C₂²	C₂×C₁₉×#126	1	1	yes	characteristic
430	C₄	—	4	4	no	—
431	C₄	—	4	4	no	—
432	C₄	—	8	2	no	—
433	C₄	C₁₉×#396	1	2	yes	—
434	C₄	C₁₉×#396	1	2	yes	—
435	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
436	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
437	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
438	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
439	C₂	—	2	2	no	—
440	C₂	—	2	2	no	—
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	C₂×C₁₉×#396	1	1	yes	characteristic
444	C₂	C₁₉×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₁₉×#2064	C₂	semidirect
154. #23603	C₁₉	direct (N × H)
204. #2064	C₂×C₁₉	semidirect
308. C₁₉	#23603	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×#430	2
C₁₉×#2911	2
C₁₉×#2905	2
C₂×C₁₉×#419	2
C₂²×C₁₉×#101	2
C₁₉×#2064	2
C₁₉×#1742	2
#23603	19

Subgroups — C19×#23603 #18029562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23603 #18029562