Subgroups — C₄×C₁₉×#328 #18014174

Order 4864.

732 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	C₄×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#328	C₂	1	2	yes	maximal
4	C₄×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1294	C₂	1	2	yes	maximal
6	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₄²×C₁₉	—	2	1	no	—
9	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₉	—	2	1	no	—
12	C₁₉×#391	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#389	C₄	1	1	yes	characteristic, complemented
14	C₁₉×#387	—	2	1	no	—
15	C₁₉×#385	—	2	1	no	—
16	C₁₉×#380	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
19	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
20	C₂×C₁₉×#95	—	2	1	no	—
21	C₂×C₁₉×#95	C₂²	1	2	yes	—
22	C₁₉×#336	—	2	1	no	—
23	C₁₉×#328	C₄	1	8	yes	direct product factor
24	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	—	2	2	no	—
26	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	—	2	2	no	—
30	C₁₉×C₂²⋊Q₈	—	2	2	no	—
31	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
32	C₄×Q₈×C₁₉	—	4	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	—	2	4	no	—
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	4	2	no	—
45	C₂×C₄²×C₁₉	—	4	2	no	—
46	C₂×C₄²×C₁₉	—	4	2	no	—
47	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₁₉×C₂²⋊C₈	—	2	2	no	—
52	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
53	C₄×C₈×C₁₉	—	4	2	no	—
54	C₁₉×#95	—	2	4	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₁₉×#95	—	2	1	no	—
59	C₁₉×#95	—	2	1	no	—
60	C₁₉×#95	—	2	2	no	—
61	C₁₉×#95	C₂×C₄	1	4	yes	—
62	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×Q₈×C₁₉	—	2	1	no	—
64	C₂×Q₈×C₁₉	—	4	1	no	—
65	C₂×Q₈×C₁₉	—	4	1	no	—
66	C₂×Q₈×C₁₉	C₄²	1	2	yes	complemented
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	4	no	—
70	C₂²×C₄×C₁₉	—	2	4	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	4	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	2	no	—
82	C₂²×C₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	—	4	2	no	—
84	C₂²×C₄×C₁₉	—	4	2	no	—
85	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
90	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	2	yes	—
95	C₂×C₈×C₁₉	—	2	4	no	—
96	C₂×C₈×C₁₉	—	4	2	no	—
97	C₂×C₈×C₁₉	—	4	2	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	2	4	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	2	no	—
103	C₄⋊C₄×C₁₉	—	4	2	no	—
104	C₄⋊C₄×C₁₉	C₄²	1	2	yes	complemented
105	C₂²⋊C₄×C₁₉	—	2	4	no	—
106	C₂²⋊C₄×C₁₉	—	4	2	no	—
107	C₄²×C₁₉	—	2	2	no	—
108	C₄²×C₁₉	—	2	2	no	—
109	C₄²×C₁₉	—	4	1	no	—
110	C₄²×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	—	4	8	no	—
112	C₄²×C₁₉	—	4	2	no	—
113	C₄²×C₁₉	—	4	2	no	—
114	C₄×#328	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₁₉	C₄×D₄	1	2	yes	—
121	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
122	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
123	C₂³×C₁₉	#135	1	2	yes	—
124	Q₈×C₁₉	—	4	2	no	—
125	Q₈×C₁₉	—	4	2	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	4	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	8	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	4	no	—
146	C₂×C₄×C₁₉	—	4	4	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	—	4	4	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	#99	1	2	yes	—
162	C₂×C₄×C₁₉	#103	1	2	yes	—
163	C₂×C₄×C₁₉	#103	1	2	yes	—
164	C₂×C₄×C₁₉	#104	1	2	yes	—
165	C₂×C₄×C₁₉	#104	1	2	yes	—
166	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
169	C₈×C₁₉	—	4	4	no	—
170	C₄×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
171	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
172	C₂×#328	C₂×C₁₉	1	2	yes	—
173	C₄×#95	C₂×C₁₉	1	1	yes	characteristic
174	#1294	C₂×C₁₉	1	2	yes	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	2	no	—
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
185	C₂²×C₁₉	#410	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
187	C₂²×C₁₉	#416	1	1	yes	characteristic
188	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
189	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
190	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
191	C₂²×C₁₉	C₄×Q₁₆	1	2	yes	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	4	8	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	—	4	1	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₄×C₁₉	#328	1	4	yes	direct product factor
204	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
205	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
206	C₂²×C₄²	—	2	1	no	—
207	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
209	C₂×C₄×C₈	—	2	1	no	—
210	#391	C₄×C₁₉	1	1	yes	characteristic, complemented
211	#389	C₄×C₁₉	1	1	yes	characteristic, complemented
212	#387	—	2	1	no	—
213	#385	—	2	1	no	—
214	#380	C₂²×C₁₉	1	1	yes	characteristic
215	C₄×C₄⋊C₄	—	2	1	no	—
216	C₄×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
217	C₄×C₂²⋊C₄	—	2	1	no	—
218	C₂×#95	—	2	1	no	—
219	C₂×#95	C₂²×C₁₉	1	2	yes	—
220	#336	—	2	1	no	—
221	#328	C₄×C₁₉	1	8	yes	direct product factor
222	C₂×C₁₉	—	2	2	no	—
223	C₂×C₁₉	—	2	2	no	—
224	C₂×C₁₉	C₂×#328	1	1	yes	characteristic
225	C₂×C₁₉	#1500	1	1	yes	characteristic
226	C₂×C₁₉	#1501	1	1	yes	characteristic
227	C₂×C₁₉	#1503	1	1	yes	characteristic
228	C₂×C₁₉	C₄×#99	1	1	yes	characteristic
229	C₂×C₁₉	C₄×#104	1	1	yes	characteristic
230	C₂×C₁₉	C₄×#103	1	1	yes	characteristic
231	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
236	C₂²×C₈	—	2	2	no	—
237	C₂²⋊Q₈	—	2	2	no	—
238	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
239	C₄×Q₈	—	4	2	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	—	2	1	no	—
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₄²	—	2	4	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	4	2	no	—
252	C₂×C₄²	—	4	2	no	—
253	C₂×C₄²	—	4	2	no	—
254	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
255	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
258	C₂²⋊C₈	—	2	2	no	—
259	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
260	C₄×C₈	—	4	2	no	—
261	#95	—	2	4	no	—
262	#95	—	2	1	no	—
263	#95	—	2	1	no	—
264	#95	—	2	1	no	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	#95	—	2	2	no	—
268	#95	C₂×C₄×C₁₉	1	4	yes	—
269	C₁₉	C₄×#328	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×Q₈	C₄²×C₁₉	1	2	yes	complemented
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
295	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
296	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
297	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
298	C₂²×C₄	Q₁₆×C₁₉	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
302	C₂²×C₄	#41×C₁₉	1	2	yes	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	—	4	2	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	C₄²×C₁₉	1	2	yes	complemented
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	4	8	no	—
320	C₄²	—	4	2	no	—
321	C₄²	—	4	2	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
327	C₂³	C₄×D₄×C₁₉	1	2	yes	—
328	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
329	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
330	C₂³	C₁₉×#135	1	2	yes	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	C₁₉×#99	1	2	yes	—
369	C₂×C₄	C₁₉×#103	1	2	yes	—
370	C₂×C₄	C₁₉×#103	1	2	yes	—
371	C₂×C₄	C₁₉×#104	1	2	yes	—
372	C₂×C₄	C₁₉×#104	1	2	yes	—
373	C₂×C₄	C₂×C₄²×C₁₉	1	1	yes	characteristic
374	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
375	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
376	C₈	—	4	4	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	C₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
386	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
387	C₂²	C₁₉×#410	1	1	yes	characteristic
388	C₂²	C₂×C₁₉×#103	1	1	yes	characteristic
389	C₂²	C₁₉×#416	1	1	yes	characteristic
390	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
391	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
392	C₂²	C₄×SD₁₆×C₁₉	1	2	yes	—
393	C₂²	C₄×Q₁₆×C₁₉	1	2	yes	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	4	8	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	2	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	1	no	—
405	C₄	C₁₉×#328	1	4	yes	direct product factor
406	C₂	—	2	2	no	—
407	C₂	—	2	2	no	—
408	C₂	C₂×C₁₉×#328	1	1	yes	characteristic
409	C₂	C₁₉×#1500	1	1	yes	characteristic
410	C₂	C₁₉×#1501	1	1	yes	characteristic
411	C₂	C₁₉×#1503	1	1	yes	characteristic
412	C₂	C₄×C₁₉×#99	1	1	yes	characteristic
413	C₂	C₄×C₁₉×#104	1	1	yes	characteristic
414	C₂	C₄×C₁₉×#103	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₂×C₄×Q₈×C₁₉	C₄	semidirect
12. C₁₉×#391	C₄	semidirect
13. C₁₉×#389	C₄	semidirect
18. C₄×C₄⋊C₄×C₁₉	C₄	semidirect
23. C₁₉×#328	C₄	direct (N × H)
66. C₂×Q₈×C₁₉	C₄²	semidirect
104. C₄⋊C₄×C₁₉	C₄²	semidirect
114. C₄×#328	C₁₉	direct (N × H)
203. C₄×C₁₉	#328	direct (N × H)
205. C₂×C₄×Q₈	C₄×C₁₉	semidirect
210. #391	C₄×C₁₉	semidirect
211. #389	C₄×C₁₉	semidirect
216. C₄×C₄⋊C₄	C₄×C₁₉	semidirect
221. #328	C₄×C₁₉	direct (N × H)
269. C₁₉	C₄×#328	direct (N × H)
274. C₂×Q₈	C₄²×C₁₉	semidirect
312. C₄⋊C₄	C₄²×C₁₉	semidirect
405. C₄	C₁₉×#328	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×C₂²⋊Q₈	2
C₄×C₁₉×C₂²⋊C₈	2
C₂×C₁₉×#328	2
C₄×C₁₉×#95	2
C₁₉×#1294	2
C₄×#328	19

Subgroups — C4×C19×#328 #18014174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#328 #18014174