Subgroups — C₁₉×#62371 #18068330

Order 4864.

1700 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3392	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3381	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3372	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3368	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3260	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3254	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3174	C₂	1	4	yes	maximal, complemented
10	C₁₉×#3167	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#564	—	2	2	no	—
13	C₁₉×#562	—	2	2	no	—
14	C₁₉×#557	—	2	2	no	—
15	C₁₉×#557	C₂²	1	4	yes	—
16	C₁₉×#557	C₂²	1	4	yes	—
17	C₁₉×#554	C₂²	1	4	yes	—
18	C₁₉×#550	C₂²	1	4	yes	—
19	C₁₉×#547	—	2	2	no	—
20	C₁₉×#541	—	2	4	no	—
21	C₁₉×#541	C₂²	1	4	yes	—
22	C₁₉×#540	C₂²	1	4	yes	—
23	C₁₉×#537	—	2	4	no	—
24	C₁₉×#533	C₂²	1	2	yes	—
25	C₁₉×#533	C₂²	1	1	yes	characteristic
26	C₁₉×#532	C₂²	1	2	yes	—
27	C₁₉×#499	C₂²	1	4	yes	—
28	C₁₉×#498	C₂²	1	2	yes	—
29	C₁₉×#492	C₂²	1	2	yes	—
30	C₁₉×#492	C₂²	1	4	yes	—
31	C₁₉×#491	C₂²	1	4	yes	—
32	C₁₉×#490	C₂²	1	4	yes	—
33	C₁₉×#487	C₂²	1	2	yes	—
34	C₁₉×#486	C₂²	1	2	yes	—
35	C₁₉×#479	C₂²	1	8	yes	—
36	C₁₉×#478	C₂²	1	8	yes	—
37	C₁₉×#477	C₂²	1	4	yes	—
38	C₁₉×#474	C₂²	1	4	yes	—
39	C₁₉×#468	C₂²	1	8	yes	—
40	C₁₉×#465	C₂²	1	4	yes	—
41	C₁₉×#465	C₂²	1	4	yes	—
42	C₁₉×#461	C₂²	1	4	yes	—
43	C₁₉×#461	C₂²	1	8	yes	—
44	C₁₉×#460	C₂²	1	4	yes	—
45	C₁₉×#460	C₂²	1	8	yes	—
46	C₁₉×#446	C₂²	1	4	yes	—
47	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
48	C₁₉×#440	C₂²	1	8	yes	—
49	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
50	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
51	C₄×SD₁₆×C₁₉	C₂²	1	8	yes	—
52	C₁₉×#424	C₂²	1	2	yes	—
53	C₁₉×#423	C₂²	1	1	yes	characteristic
54	C₁₉×#405	C₂²	1	2	yes	—
55	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
56	C₂×#41×C₁₉	—	2	4	no	—
57	C₂×#41×C₁₉	—	2	2	no	—
58	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
59	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
60	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
61	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	—	2	4	no	—
65	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
66	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₉×#127	C₂³	1	2	yes	—
71	C₁₉×#127	C₂³	1	4	yes	—
72	C₁₉×#126	—	2	8	no	—
73	C₁₉×#125	—	2	4	no	—
74	C₁₉×#125	—	2	8	no	—
75	C₁₉×#125	—	2	8	no	—
76	C₁₉×#125	—	2	8	no	—
77	C₁₉×#125	—	2	2	no	—
78	C₁₉×#125	D₄	1	2	yes	—
79	C₁₉×#125	C₂³	1	4	yes	—
80	C₁₉×#125	C₂³	1	4	yes	—
81	C₁₉×#124	—	2	2	no	—
82	C₁₉×#123	—	2	8	no	—
83	C₁₉×C₂²⋊Q₈	—	2	4	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	8	no	—
86	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
87	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	4	no	—
90	C₁₉×#121	—	2	8	no	—
91	C₁₉×#121	—	2	8	no	—
92	C₁₉×#121	C₂³	1	4	yes	—
93	C₄×Q₈×C₁₉	—	2	4	no	—
94	C₄×Q₈×C₁₉	—	2	4	no	—
95	C₄×Q₈×C₁₉	—	2	2	no	—
96	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
97	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
98	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	C₂³	1	4	yes	—
101	C₄×D₄×C₁₉	C₂³	1	8	yes	—
102	C₁₉×#117	—	2	2	no	—
103	C₁₉×#117	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×#107	C₂³	1	8	yes	—
107	C₁₉×#106	C₂³	1	4	yes	—
108	C₁₉×#106	C₂³	1	4	yes	—
109	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
110	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
111	C₁₉×#103	C₂³	1	4	yes	—
112	C₁₉×#103	C₂³	1	4	yes	—
113	C₁₉×#103	C₂³	1	8	yes	—
114	C₁₉×#102	C₂³	1	4	yes	—
115	C₁₉×#102	C₂³	1	4	yes	—
116	C₁₉×#102	C₂³	1	8	yes	—
117	C₁₉×#97	C₂³	1	4	yes	—
118	C₄×C₈×C₁₉	C₂³	1	2	yes	—
119	C₄×C₈×C₁₉	C₂³	1	2	yes	—
120	C₄×C₈×C₁₉	C₂³	1	4	yes	—
121	#41×C₁₉	—	8	4	no	—
122	#41×C₁₉	—	8	8	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	2	no	—
125	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
126	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
127	C₂×D₄×C₁₉	—	2	4	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	8	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₉	—	2	4	no	—
133	C₂²×C₄×C₁₉	—	2	8	no	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	SD₁₆×C₁₉	—	2	8	no	—
137	SD₁₆×C₁₉	—	4	4	no	—
138	SD₁₆×C₁₉	—	4	8	no	—
139	M₁₆×C₁₉	—	4	2	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	4	1	no	—
142	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
143	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
145	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	8	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	4	no	—
152	C₄⋊C₄×C₁₉	—	2	8	no	—
153	C₄⋊C₄×C₁₉	—	2	8	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	8	no	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
157	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
158	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
159	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
160	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
161	C₂²⋊C₄×C₁₉	—	2	4	no	—
162	C₂²⋊C₄×C₁₉	—	2	4	no	—
163	C₂²⋊C₄×C₁₉	—	2	8	no	—
164	C₂²⋊C₄×C₁₉	—	2	4	no	—
165	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
166	C₄²×C₁₉	—	2	4	no	—
167	C₄²×C₁₉	—	2	8	no	—
168	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂⁴	1	2	yes	—
171	C₄²×C₁₉	C₂⁴	1	4	yes	—
172	#62371	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	4	no	—
174	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₉	—	2	8	no	—
176	Q₈×C₁₉	—	2	4	no	—
177	Q₈×C₁₉	—	2	4	no	—
178	Q₈×C₁₉	—	4	4	no	—
179	Q₈×C₁₉	—	8	2	no	—
180	D₄×C₁₉	—	2	4	no	—
181	D₄×C₁₉	—	2	4	no	—
182	D₄×C₁₉	—	4	4	no	—
183	D₄×C₁₉	—	8	2	no	—
184	D₄×C₁₉	—	8	8	no	—
185	D₄×C₁₉	—	8	4	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	4	8	no	—
193	C₂×C₄×C₁₉	—	8	8	no	—
194	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
199	C₈×C₁₉	—	2	1	no	—
200	C₈×C₁₉	—	2	2	no	—
201	C₈×C₁₉	—	2	4	no	—
202	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
203	#3556	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#3548	C₂×C₁₉	1	1	yes	characteristic
205	#3392	C₂×C₁₉	1	4	yes	complemented
206	#3381	C₂×C₁₉	1	4	yes	complemented
207	#3372	C₂×C₁₉	1	4	yes	complemented
208	#3368	C₂×C₁₉	1	4	yes	complemented
209	#3260	C₂×C₁₉	1	4	yes	complemented
210	#3254	C₂×C₁₉	1	2	yes	complemented
211	#3174	C₂×C₁₉	1	4	yes	complemented
212	#3167	C₂×C₁₉	1	2	yes	complemented
213	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	4	4	no	—
217	C₂²×C₁₉	—	4	4	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	2	8	no	—
223	C₄×C₁₉	—	4	4	no	—
224	C₄×C₁₉	—	4	4	no	—
225	C₄×C₁₉	—	4	4	no	—
226	C₄×C₁₉	#577	1	4	yes	—
227	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
228	C₄×C₁₉	#585	1	1	yes	characteristic
229	#564	—	2	2	no	—
230	#562	—	2	2	no	—
231	#557	—	2	2	no	—
232	#557	C₂²×C₁₉	1	4	yes	—
233	#557	C₂²×C₁₉	1	4	yes	—
234	#554	C₂²×C₁₉	1	4	yes	—
235	#550	C₂²×C₁₉	1	4	yes	—
236	#547	—	2	2	no	—
237	#541	—	2	4	no	—
238	#541	C₂²×C₁₉	1	4	yes	—
239	#540	C₂²×C₁₉	1	4	yes	—
240	#537	—	2	4	no	—
241	#533	C₂²×C₁₉	1	2	yes	—
242	#533	C₂²×C₁₉	1	1	yes	characteristic
243	#532	C₂²×C₁₉	1	2	yes	—
244	#499	C₂²×C₁₉	1	4	yes	—
245	#498	C₂²×C₁₉	1	2	yes	—
246	#492	C₂²×C₁₉	1	2	yes	—
247	#492	C₂²×C₁₉	1	4	yes	—
248	#491	C₂²×C₁₉	1	4	yes	—
249	#490	C₂²×C₁₉	1	4	yes	—
250	#487	C₂²×C₁₉	1	2	yes	—
251	#486	C₂²×C₁₉	1	2	yes	—
252	#479	C₂²×C₁₉	1	8	yes	—
253	#478	C₂²×C₁₉	1	8	yes	—
254	#477	C₂²×C₁₉	1	4	yes	—
255	#474	C₂²×C₁₉	1	4	yes	—
256	#468	C₂²×C₁₉	1	8	yes	—
257	#465	C₂²×C₁₉	1	4	yes	—
258	#465	C₂²×C₁₉	1	4	yes	—
259	#461	C₂²×C₁₉	1	4	yes	—
260	#461	C₂²×C₁₉	1	8	yes	—
261	#460	C₂²×C₁₉	1	4	yes	—
262	#460	C₂²×C₁₉	1	8	yes	—
263	#446	C₂²×C₁₉	1	4	yes	—
264	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
265	#440	C₂²×C₁₉	1	8	yes	—
266	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
267	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
268	C₄×SD₁₆	C₂²×C₁₉	1	8	yes	—
269	#424	C₂²×C₁₉	1	2	yes	—
270	#423	C₂²×C₁₉	1	1	yes	characteristic
271	#405	C₂²×C₁₉	1	2	yes	—
272	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×C₁₉	—	4	1	no	—
274	C₂×C₁₉	—	8	4	no	—
275	C₂×C₁₉	#3497	1	1	yes	characteristic
276	C₂×C₁₉	C₂×#577	1	2	yes	—
277	C₂×#41	—	2	4	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
280	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
281	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
282	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
283	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
285	C₄⋊Q₈	—	2	4	no	—
286	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
287	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
288	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
289	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
290	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
291	#127	C₂³×C₁₉	1	2	yes	—
292	#127	C₂³×C₁₉	1	4	yes	—
293	#126	—	2	8	no	—
294	#125	—	2	4	no	—
295	#125	—	2	8	no	—
296	#125	—	2	8	no	—
297	#125	—	2	8	no	—
298	#125	—	2	2	no	—
299	#125	D₄×C₁₉	1	2	yes	—
300	#125	C₂³×C₁₉	1	4	yes	—
301	#125	C₂³×C₁₉	1	4	yes	—
302	#124	—	2	2	no	—
303	#123	—	2	8	no	—
304	C₂²⋊Q₈	—	2	4	no	—
305	C₂²⋊Q₈	—	2	2	no	—
306	C₂²⋊Q₈	—	2	8	no	—
307	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
308	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
309	#121	—	2	2	no	—
310	#121	—	2	4	no	—
311	#121	—	2	8	no	—
312	#121	—	2	8	no	—
313	#121	C₂³×C₁₉	1	4	yes	—
314	C₄×Q₈	—	2	4	no	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
318	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
319	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	C₂³×C₁₉	1	4	yes	—
322	C₄×D₄	C₂³×C₁₉	1	8	yes	—
323	#117	—	2	2	no	—
324	#117	C₂³×C₁₉	1	2	yes	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
327	#107	C₂³×C₁₉	1	8	yes	—
328	#106	C₂³×C₁₉	1	4	yes	—
329	#106	C₂³×C₁₉	1	4	yes	—
330	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
331	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
332	#103	C₂³×C₁₉	1	4	yes	—
333	#103	C₂³×C₁₉	1	4	yes	—
334	#103	C₂³×C₁₉	1	8	yes	—
335	#102	C₂³×C₁₉	1	4	yes	—
336	#102	C₂³×C₁₉	1	4	yes	—
337	#102	C₂³×C₁₉	1	8	yes	—
338	#97	C₂³×C₁₉	1	4	yes	—
339	C₄×C₈	C₂³×C₁₉	1	2	yes	—
340	C₄×C₈	C₂³×C₁₉	1	2	yes	—
341	C₄×C₈	C₂³×C₁₉	1	4	yes	—
342	C₁₉	#62371	1	1	yes	characteristic, direct product factor, Sylow
343	#41	—	8	4	no	—
344	#41	—	8	8	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
348	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	8	no	—
356	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
358	SD₁₆	—	2	8	no	—
359	SD₁₆	—	4	4	no	—
360	SD₁₆	—	4	8	no	—
361	M₁₆	—	4	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
365	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
366	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
367	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
379	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
380	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
381	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
382	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	8	no	—
390	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₄²	C₂⁴×C₁₉	1	2	yes	—
393	C₄²	C₂⁴×C₁₉	1	4	yes	—
394	C₂³	—	2	4	no	—
395	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
396	Q₈	—	2	8	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	2	4	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	8	2	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	4	4	no	—
404	D₄	—	8	2	no	—
405	D₄	—	8	8	no	—
406	D₄	—	8	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	8	8	no	—
415	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
416	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
419	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	2	2	no	—
422	C₈	—	2	4	no	—
423	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	8	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	4	no	—
436	C₄	C₁₉×#577	1	4	yes	—
437	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
438	C₄	C₁₉×#585	1	1	yes	characteristic
439	C₂	—	4	1	no	—
440	C₂	—	8	4	no	—
441	C₂	C₁₉×#3497	1	1	yes	characteristic
442	C₂	C₂×C₁₉×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3556	C₂	semidirect
3. C₁₉×#3392	C₂	semidirect
4. C₁₉×#3381	C₂	semidirect
5. C₁₉×#3372	C₂	semidirect
6. C₁₉×#3368	C₂	semidirect
7. C₁₉×#3260	C₂	semidirect
8. C₁₉×#3254	C₂	semidirect
9. C₁₉×#3174	C₂	semidirect
10. C₁₉×#3167	C₂	semidirect
11. C₁₉×#2960	C₂	semidirect
172. #62371	C₁₉	direct (N × H)
203. #3556	C₂×C₁₉	semidirect
205. #3392	C₂×C₁₉	semidirect
206. #3381	C₂×C₁₉	semidirect
207. #3372	C₂×C₁₉	semidirect
208. #3368	C₂×C₁₉	semidirect
209. #3260	C₂×C₁₉	semidirect
210. #3254	C₂×C₁₉	semidirect
211. #3174	C₂×C₁₉	semidirect
212. #3167	C₂×C₁₉	semidirect
213. #2960	C₂×C₁₉	semidirect
342. C₁₉	#62371	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×#3556	2
C₁₉×#3548	2
C₁₉×#3392	2
C₁₉×#3381	2
C₁₉×#3372	2
C₁₉×#3368	2
C₁₉×#3260	2
C₁₉×#3254	2
C₁₉×#3174	2
C₁₉×#3167	2
C₁₉×#2960	2
#62371	19

Subgroups — C19×#62371 #18068330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62371 #18068330