Subgroups — C₁₉×#3271 #14561128

Order 2432.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#137	—	2	4	no	—
21	C₁₉×#135	—	2	4	no	—
22	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#127	—	2	1	no	—
34	C₁₉×#127	C₂²	1	1	yes	characteristic
35	C₁₉×#124	—	2	1	no	—
36	C₁₉×#124	C₂²	1	1	yes	characteristic
37	C₁₉×C₂²⋊Q₈	—	2	1	no	—
38	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₁₉×#121	—	2	1	no	—
40	C₁₉×#121	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₁₉×#121	C₂²	1	1	yes	characteristic
43	C₁₉×#121	C₂²	1	1	yes	characteristic
44	C₁₉×#121	C₂²	1	1	yes	characteristic
45	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×D₄×C₁₉	—	2	1	no	—
48	C₄×D₄×C₁₉	—	2	1	no	—
49	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#106	C₂²	1	1	yes	characteristic
51	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₁₉×#103	C₂²	1	1	yes	characteristic
53	C₁₉×#103	C₂²	1	1	yes	characteristic
54	C₁₉×#103	C₂²	1	1	yes	characteristic
55	C₁₉×#102	C₂²	1	1	yes	characteristic
56	C₁₉×#102	C₂²	1	1	yes	characteristic
57	C₁₉×#102	C₂²	1	1	yes	characteristic
58	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₁₉×#97	C₂²	1	1	yes	characteristic
61	#41×C₁₉	—	2	2	no	—
62	#41×C₁₉	—	2	2	no	—
63	#41×C₁₉	—	2	2	no	—
64	#41×C₁₉	—	4	1	no	—
65	#41×C₁₉	—	4	1	no	—
66	#41×C₁₉	—	4	1	no	—
67	C₂×Q₈×C₁₉	—	2	1	no	—
68	C₂×Q₈×C₁₉	—	2	2	no	—
69	C₂×Q₈×C₁₉	—	4	1	no	—
70	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×D₄×C₁₉	—	2	1	no	—
74	C₂×D₄×C₁₉	—	2	1	no	—
75	C₂×D₄×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	2	1	no	—
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
82	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	Q₁₆×C₁₉	—	2	2	no	—
92	Q₁₆×C₁₉	D₄	1	4	yes	complemented
93	SD₁₆×C₁₉	—	2	2	no	—
94	SD₁₆×C₁₉	—	2	2	no	—
95	SD₁₆×C₁₉	—	2	2	no	—
96	SD₁₆×C₁₉	—	2	2	no	—
97	SD₁₆×C₁₉	—	4	1	no	—
98	D₈×C₁₉	—	2	2	no	—
99	D₈×C₁₉	—	4	1	no	—
100	M₁₆×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
110	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
120	C₄²×C₁₉	—	2	1	no	—
121	C₄²×C₁₉	—	2	1	no	—
122	C₄²×C₁₉	C₂³	1	1	yes	characteristic
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
128	Q₈×C₁₉	—	2	1	no	—
129	Q₈×C₁₉	—	2	1	no	—
130	Q₈×C₁₉	—	2	1	no	—
131	Q₈×C₁₉	—	2	1	no	—
132	Q₈×C₁₉	—	4	2	no	—
133	Q₈×C₁₉	C₂×D₄	1	2	yes	—
134	Q₈×C₁₉	C₂×D₄	1	2	yes	—
135	D₄×C₁₉	—	2	1	no	—
136	D₄×C₁₉	—	2	1	no	—
137	D₄×C₁₉	—	2	1	no	—
138	D₄×C₁₉	—	2	1	no	—
139	D₄×C₁₉	—	2	1	no	—
140	D₄×C₁₉	—	2	1	no	—
141	D₄×C₁₉	—	4	1	no	—
142	D₄×C₁₉	—	4	2	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	4	2	no	—
145	D₄×C₁₉	—	4	2	no	—
146	D₄×C₁₉	—	4	2	no	—
147	D₄×C₁₉	—	8	1	no	—
148	D₄×C₁₉	—	8	1	no	—
149	D₄×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
168	C₈×C₁₉	—	2	1	no	—
169	C₈×C₁₉	—	2	1	no	—
170	C₈×C₁₉	—	2	1	no	—
171	C₈×C₁₉	C₂×D₄	1	2	yes	—
172	#3271	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	4	1	no	—
180	C₂²×C₁₉	—	4	1	no	—
181	C₂²×C₁₉	—	4	1	no	—
182	C₂²×C₁₉	—	4	1	no	—
183	C₂²×C₁₉	—	4	1	no	—
184	C₂²×C₁₉	—	4	1	no	—
185	C₂²×C₁₉	—	4	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	2	2	no	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	4	1	no	—
196	C₄×C₁₉	—	4	1	no	—
197	C₄×C₁₉	—	4	1	no	—
198	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
199	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×#137	C₂×C₁₉	1	1	yes	characteristic, complemented
201	C₂×#135	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#550	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#548	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#496	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#469	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#465	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#464	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#460	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#452	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#449	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#449	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#448	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#441	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#435	C₂×C₁₉	1	1	yes	characteristic, complemented
215	C₂×C₁₉	—	4	1	no	—
216	C₂×C₁₉	—	4	1	no	—
217	C₂×C₁₉	—	8	1	no	—
218	C₂×C₁₉	—	8	1	no	—
219	C₂×C₁₉	—	8	1	no	—
220	C₂×C₁₉	D₄²	1	1	yes	characteristic
221	C₂×C₁₉	#575	1	1	yes	characteristic
222	C₂×C₁₉	#577	1	1	yes	characteristic
223	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
226	C₂²×Q₈	C₂²×C₁₉	1	1	yes	characteristic
227	#137	—	2	4	no	—
228	#135	—	2	4	no	—
229	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
231	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
239	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
240	#127	—	2	1	no	—
241	#127	C₂²×C₁₉	1	1	yes	characteristic
242	#124	—	2	1	no	—
243	#124	C₂²×C₁₉	1	1	yes	characteristic
244	C₂²⋊Q₈	—	2	1	no	—
245	C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
246	#121	—	2	1	no	—
247	#121	—	2	1	no	—
248	#121	—	2	1	no	—
249	#121	C₂²×C₁₉	1	1	yes	characteristic
250	#121	C₂²×C₁₉	1	1	yes	characteristic
251	#121	C₂²×C₁₉	1	1	yes	characteristic
252	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
253	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
257	#106	C₂²×C₁₉	1	1	yes	characteristic
258	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
259	#103	C₂²×C₁₉	1	1	yes	characteristic
260	#103	C₂²×C₁₉	1	1	yes	characteristic
261	#103	C₂²×C₁₉	1	1	yes	characteristic
262	#102	C₂²×C₁₉	1	1	yes	characteristic
263	#102	C₂²×C₁₉	1	1	yes	characteristic
264	#102	C₂²×C₁₉	1	1	yes	characteristic
265	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
266	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
267	#97	C₂²×C₁₉	1	1	yes	characteristic
268	C₁₉	#3271	1	1	yes	characteristic, direct product factor, Sylow
269	#41	—	2	2	no	—
270	#41	—	2	2	no	—
271	#41	—	2	2	no	—
272	#41	—	4	1	no	—
273	#41	—	4	1	no	—
274	#41	—	4	1	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
279	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
280	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	D₄×C₁₉	1	1	yes	characteristic
290	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
292	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
298	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
299	Q₁₆	—	2	2	no	—
300	Q₁₆	D₄×C₁₉	1	4	yes	complemented
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	2	2	no	—
303	SD₁₆	—	2	2	no	—
304	SD₁₆	—	2	2	no	—
305	SD₁₆	—	4	1	no	—
306	D₈	—	2	2	no	—
307	D₈	—	4	1	no	—
308	M₁₆	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
313	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
318	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
319	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
320	C₂²⋊C₄	—	2	1	no	—
321	C₂²⋊C₄	—	2	1	no	—
322	C₂²⋊C₄	—	2	1	no	—
323	C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
327	C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	C₂³×C₁₉	1	1	yes	characteristic
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
336	Q₈	—	2	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	2	1	no	—
339	Q₈	—	2	1	no	—
340	Q₈	—	4	2	no	—
341	Q₈	C₂×D₄×C₁₉	1	2	yes	—
342	Q₈	C₂×D₄×C₁₉	1	2	yes	—
343	D₄	—	2	1	no	—
344	D₄	—	2	1	no	—
345	D₄	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	C₂×D₄×C₁₉	1	2	yes	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
406	C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂	—	4	1	no	—
408	C₂	—	4	1	no	—
409	C₂	—	8	1	no	—
410	C₂	—	8	1	no	—
411	C₂	—	8	1	no	—
412	C₂	D₄²×C₁₉	1	1	yes	characteristic
413	C₂	C₁₉×#575	1	1	yes	characteristic
414	C₂	C₁₉×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#137	C₂	semidirect
2. C₂×C₁₉×#135	C₂	semidirect
3. C₁₉×#550	C₂	semidirect
4. C₁₉×#548	C₂	semidirect
5. C₁₉×#496	C₂	semidirect
6. C₁₉×#469	C₂	semidirect
7. C₁₉×#465	C₂	semidirect
8. C₁₉×#464	C₂	semidirect
9. C₁₉×#460	C₂	semidirect
10. C₁₉×#452	C₂	semidirect
11. C₁₉×#449	C₂	semidirect
12. C₁₉×#449	C₂	semidirect
13. C₁₉×#448	C₂	semidirect
14. C₁₉×#441	C₂	semidirect
15. C₁₉×#435	C₂	semidirect
92. Q₁₆×C₁₉	D₄	semidirect
172. #3271	C₁₉	direct (N × H)
200. C₂×#137	C₂×C₁₉	semidirect
201. C₂×#135	C₂×C₁₉	semidirect
202. #550	C₂×C₁₉	semidirect
203. #548	C₂×C₁₉	semidirect
204. #496	C₂×C₁₉	semidirect
205. #469	C₂×C₁₉	semidirect
206. #465	C₂×C₁₉	semidirect
207. #464	C₂×C₁₉	semidirect
208. #460	C₂×C₁₉	semidirect
209. #452	C₂×C₁₉	semidirect
210. #449	C₂×C₁₉	semidirect
211. #449	C₂×C₁₉	semidirect
212. #448	C₂×C₁₉	semidirect
213. #441	C₂×C₁₉	semidirect
214. #435	C₂×C₁₉	semidirect
268. C₁₉	#3271	direct (N × H)
300. Q₁₆	D₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#137	2
C₂×C₁₉×#135	2
C₁₉×#550	2
C₁₉×#548	2
C₁₉×#496	2
C₁₉×#469	2
C₁₉×#465	2
C₁₉×#464	2
C₁₉×#460	2
C₁₉×#452	2
C₁₉×#449	2
C₁₉×#448	2
C₁₉×#441	2
C₁₉×#435	2
#3271	19

Subgroups — C19×#3271 #14561128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3271 #14561128