Subgroups — #340×Dic₁₉ #18087718

Order 4864.

1182 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×Dic₁₉	C₂	1	2	yes	maximal
3	C₂×#11926307	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926306	C₂	1	2	yes	maximal
5	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₁₉	—	2	2	no	—
9	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₈×Dic₁₉	—	2	4	no	—
11	C₂×C₈×Dic₁₉	C₄	1	4	yes	complemented
12	C₄⋊C₄×Dic₁₉	—	2	4	no	—
13	C₄⋊C₄×Dic₁₉	C₄	1	8	yes	complemented
14	C₂×C₁₉⋊#95	—	2	2	no	—
15	#11926307	C₄	1	4	yes	complemented
16	#11926306	C₄	1	8	yes	complemented
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#340	C₄	1	4	yes	complemented
20	C₂³×C₄×C₁₉	—	2	2	no	—
21	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂³×Dic₁₉	—	2	2	no	—
23	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
24	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	—	2	2	no	—
26	C₂²×C₈×C₁₉	—	2	2	no	—
27	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
36	C₂×C₄⋊Dic₁₉	—	2	2	no	—
37	C₂×C₄⋊Dic₁₉	—	2	2	no	—
38	C₂×C₄⋊Dic₁₉	—	2	2	no	—
39	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
40	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
41	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
42	C₂×C₄×Dic₁₉	—	2	8	no	—
43	C₂×C₄×Dic₁₉	—	4	4	no	—
44	C₂×C₄×Dic₁₉	—	4	4	no	—
45	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
46	C₂×C₄×Dic₁₉	C₂×C₄	1	4	yes	—
47	C₂×C₄×Dic₁₉	D₄	1	4	yes	—
48	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
53	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
54	C₁₉⋊#95	—	2	8	no	—
55	C₈×Dic₁₉	—	2	8	no	—
56	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	—	2	4	no	—
58	C₂²×C₄×C₁₉	—	2	4	no	—
59	C₂²×C₄×C₁₉	—	2	4	no	—
60	C₂²×C₄×C₁₉	—	4	2	no	—
61	C₂²×C₄×C₁₉	—	4	2	no	—
62	C₂²×C₄×C₁₉	—	4	2	no	—
63	C₂²×C₄×C₁₉	—	4	2	no	—
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
66	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
70	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	#41	1	2	yes	—
73	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
74	C₂²×Dic₁₉	—	2	1	no	—
75	C₂²×Dic₁₉	—	2	2	no	—
76	C₂²×Dic₁₉	—	2	1	no	—
77	C₂²×Dic₁₉	—	2	4	no	—
78	C₂²×Dic₁₉	—	2	4	no	—
79	C₂²×Dic₁₉	—	2	4	no	—
80	C₂²×Dic₁₉	—	4	2	no	—
81	C₂²×Dic₁₉	—	4	2	no	—
82	C₂²×Dic₁₉	—	4	2	no	—
83	C₂²×Dic₁₉	—	4	2	no	—
84	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
85	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
86	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
87	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
88	C₂²×Dic₁₉	D₈	1	2	yes	—
89	C₂²×Dic₁₉	SD₁₆	1	4	yes	—
90	C₂²×Dic₁₉	Q₁₆	1	2	yes	—
91	C₂×C₈×C₁₉	—	2	2	no	—
92	C₂×C₈×C₁₉	—	2	2	no	—
93	C₂×C₈×C₁₉	—	2	4	no	—
94	C₂×C₈×C₁₉	—	2	4	no	—
95	C₂×C₈×C₁₉	C₄²	1	4	yes	complemented
96	C₄⋊C₄×C₁₉	—	2	4	no	—
97	C₄⋊C₄×C₁₉	—	2	4	no	—
98	C₄⋊C₄×C₁₉	—	2	4	no	—
99	C₄⋊C₄×C₁₉	C₄²	1	8	yes	complemented
100	C₄⋊Dic₁₉	—	2	4	no	—
101	C₄⋊Dic₁₉	—	2	4	no	—
102	C₄⋊Dic₁₉	—	2	4	no	—
103	C₄⋊Dic₁₉	C₄²	1	8	yes	complemented
104	C₄×Dic₁₉	—	4	16	no	—
105	C₄×Dic₁₉	C₄²	1	4	yes	—
106	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
107	C₄×Dic₁₉	C₄⋊C₄	1	8	yes	—
108	C₂×C₁₉⋊C₈	—	2	2	no	—
109	C₂×C₁₉⋊C₈	—	2	2	no	—
110	C₂×C₁₉⋊C₈	—	2	4	no	—
111	C₂×C₁₉⋊C₈	—	2	4	no	—
112	C₂×C₁₉⋊C₈	C₄²	1	4	yes	complemented
113	C₄×#340	—	19	1	no	maximal, Sylow
114	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
115	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
116	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
117	C₂³×C₁₉	C₄×D₄	1	2	yes	—
118	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
119	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
120	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
121	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
122	C₂³×C₁₉	#135	1	1	yes	characteristic
123	C₂³×C₁₉	#135	1	2	yes	—
124	C₂³×C₁₉	#135	1	1	yes	characteristic
125	C₂×C₄×C₁₉	—	2	8	no	—
126	C₂×C₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	4	4	no	—
128	C₂×C₄×C₁₉	—	4	4	no	—
129	C₂×C₄×C₁₉	—	4	4	no	—
130	C₂×C₄×C₁₉	—	4	4	no	—
131	C₂×C₄×C₁₉	—	4	4	no	—
132	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
133	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
136	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
137	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#117	1	2	yes	—
141	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#117	1	2	yes	—
143	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
145	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
147	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
150	C₂×Dic₁₉	—	2	4	no	—
151	C₂×Dic₁₉	—	2	4	no	—
152	C₂×Dic₁₉	—	2	2	no	—
153	C₂×Dic₁₉	—	2	2	no	—
154	C₂×Dic₁₉	—	2	8	no	—
155	C₂×Dic₁₉	—	4	4	no	—
156	C₂×Dic₁₉	—	4	4	no	—
157	C₂×Dic₁₉	—	4	4	no	—
158	C₂×Dic₁₉	—	4	4	no	—
159	C₂×Dic₁₉	—	4	4	no	—
160	C₂×Dic₁₉	—	4	4	no	—
161	C₂×Dic₁₉	#95	1	4	yes	—
162	C₂×Dic₁₉	#95	1	4	yes	—
163	C₂×Dic₁₉	#102	1	8	yes	—
164	C₂×Dic₁₉	#103	1	8	yes	—
165	C₂×Dic₁₉	#106	1	4	yes	—
166	C₂×Dic₁₉	#107	1	4	yes	—
167	C₈×C₁₉	—	2	4	no	—
168	C₁₉⋊C₈	—	2	4	no	—
169	C₂²×C₄×C₈	—	19	1	no	—
170	C₂×C₄×C₄⋊C₄	—	19	2	no	—
171	C₂×#340	—	19	1	no	—
172	C₂×#340	—	19	2	no	—
173	C₂×#340	D₁₉	1	1	yes	characteristic
174	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
175	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
176	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
177	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
179	C₂²×C₁₉	C₂×#102	1	2	yes	—
180	C₂²×C₁₉	C₂×#103	1	2	yes	—
181	C₂²×C₁₉	#416	1	2	yes	—
182	C₂²×C₁₉	#416	1	2	yes	—
183	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
184	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
185	C₂²×C₁₉	#427	1	1	yes	characteristic
186	C₂²×C₁₉	#427	1	1	yes	characteristic
187	C₂²×C₁₉	C₄×D₈	1	2	yes	—
188	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
189	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
190	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
191	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
192	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
193	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
194	C₂²×C₁₉	C₄×Q₁₆	1	2	yes	—
195	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
196	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
197	C₄×C₁₉	—	4	8	no	—
198	C₄×C₁₉	C₄³	1	1	yes	characteristic
199	C₄×C₁₉	#376	1	1	yes	characteristic
200	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
201	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
202	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
203	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
204	Dic₁₉	—	2	4	no	—
205	Dic₁₉	—	4	8	no	—
206	Dic₁₉	#340	1	8	yes	direct product factor
207	C₂³×C₈	—	19	1	no	—
208	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	—	19	2	no	—
210	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
211	C₂²×C₄²	—	19	1	no	—
212	C₂²×C₄²	—	38	2	no	—
213	C₂×C₄×C₈	—	19	4	no	—
214	C₂×C₄×C₈	—	38	4	no	—
215	C₄×C₄⋊C₄	—	19	8	no	—
216	C₄×C₄⋊C₄	—	38	4	no	—
217	C₂×#95	—	38	2	no	—
218	#340	—	19	4	no	—
219	#340	—	19	8	no	—
220	#340	Dic₁₉	1	4	yes	direct product factor
221	C₂×C₁₉	C₄×#95	1	1	yes	characteristic
222	C₂×C₁₉	C₂×#340	1	1	yes	characteristic
223	C₂×C₁₉	#1735	1	1	yes	characteristic
224	C₂×C₁₉	C₄×#102	1	2	yes	—
225	C₂×C₁₉	C₄×#102	1	2	yes	—
226	C₂×C₁₉	C₄×#103	1	2	yes	—
227	C₂×C₁₉	C₄×#103	1	2	yes	—
228	C₂×C₁₉	C₄×#106	1	1	yes	characteristic
229	C₂×C₁₉	C₄×#106	1	1	yes	characteristic
230	C₂×C₁₉	C₄×#107	1	1	yes	characteristic
231	C₂×C₁₉	C₄×#107	1	1	yes	characteristic
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	—	19	1	no	—
234	C₂³×C₄	—	19	1	no	—
235	C₂³×C₄	—	38	2	no	—
236	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	19	4	no	—
240	C₂²×C₈	—	19	2	no	—
241	C₂²×C₈	—	38	2	no	—
242	C₂²×C₈	—	38	1	no	—
243	C₂²×C₈	—	38	1	no	—
244	C₂²×C₈	C₄×D₁₉	1	2	yes	—
245	C₂²×C₈	C₄×D₁₉	1	2	yes	—
246	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	19	4	no	—
251	C₂×C₄⋊C₄	—	19	4	no	—
252	C₂×C₄⋊C₄	—	19	4	no	—
253	C₂×C₄⋊C₄	—	38	2	no	—
254	C₂×C₄⋊C₄	—	38	2	no	—
255	C₂×C₄⋊C₄	—	38	2	no	—
256	C₂×C₄⋊C₄	C₄×D₁₉	1	4	yes	—
257	C₂×C₄⋊C₄	C₄×D₁₉	1	4	yes	—
258	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
259	C₂×C₄²	—	19	4	no	—
260	C₂×C₄²	—	19	2	no	—
261	C₂×C₄²	—	19	4	no	—
262	C₂×C₄²	—	19	2	no	—
263	C₂×C₄²	—	38	8	no	—
264	C₂×C₄²	—	76	4	no	—
265	C₂×C₄²	—	76	4	no	—
266	C₄×C₈	—	38	8	no	—
267	#95	—	38	8	no	—
268	C₁₉	C₄×#340	1	1	yes	characteristic, complemented, Sylow
269	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	19	4	no	—
278	C₂²×C₄	—	19	2	no	—
279	C₂²×C₄	—	19	2	no	—
280	C₂²×C₄	—	19	4	no	—
281	C₂²×C₄	—	19	2	no	—
282	C₂²×C₄	—	19	4	no	—
283	C₂²×C₄	—	19	2	no	—
284	C₂²×C₄	—	38	1	no	—
285	C₂²×C₄	—	38	2	no	—
286	C₂²×C₄	—	38	1	no	—
287	C₂²×C₄	—	38	4	no	—
288	C₂²×C₄	—	38	4	no	—
289	C₂²×C₄	—	38	4	no	—
290	C₂²×C₄	—	76	2	no	—
291	C₂²×C₄	—	76	2	no	—
292	C₂²×C₄	—	76	2	no	—
293	C₂²×C₄	—	76	2	no	—
294	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
296	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
298	C₂²×C₄	D₄×D₁₉	1	2	yes	—
299	C₂²×C₄	#64543	1	2	yes	—
300	C₂²×C₄	#64543	1	1	yes	characteristic
301	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
302	C₂²×C₄	#64545	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	19	4	no	—
309	C₂×C₈	—	38	2	no	—
310	C₂×C₈	—	38	4	no	—
311	C₂×C₈	—	38	2	no	—
312	C₂×C₈	—	38	4	no	—
313	C₂×C₈	C₄×Dic₁₉	1	4	yes	complemented
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	19	8	no	—
318	C₄⋊C₄	—	38	4	no	—
319	C₄⋊C₄	—	38	4	no	—
320	C₄⋊C₄	—	38	4	no	—
321	C₄⋊C₄	C₄×Dic₁₉	1	8	yes	complemented
322	C₄²	—	19	4	no	—
323	C₄²	—	19	4	no	—
324	C₄²	—	19	8	no	—
325	C₄²	—	76	16	no	—
326	C₂³	C₂²⋊C₄×D₁₉	1	2	yes	—
327	C₂³	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
328	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
329	C₂³	#10597339	1	1	yes	characteristic
330	C₂³	D₈×D₁₉	1	1	yes	characteristic
331	C₂³	#10597358	1	1	yes	characteristic
332	C₂³	SD₁₆×D₁₉	1	2	yes	—
333	C₂³	#10597362	1	2	yes	—
334	C₂³	Q₁₆×D₁₉	1	1	yes	characteristic
335	C₂³	#10597365	1	1	yes	characteristic
336	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	19	8	no	—
345	C₂×C₄	—	19	8	no	—
346	C₂×C₄	—	19	4	no	—
347	C₂×C₄	—	19	4	no	—
348	C₂×C₄	—	19	4	no	—
349	C₂×C₄	—	19	4	no	—
350	C₂×C₄	—	38	4	no	—
351	C₂×C₄	—	38	4	no	—
352	C₂×C₄	—	38	2	no	—
353	C₂×C₄	—	38	2	no	—
354	C₂×C₄	—	38	8	no	—
355	C₂×C₄	—	76	4	no	—
356	C₂×C₄	—	76	4	no	—
357	C₂×C₄	—	76	4	no	—
358	C₂×C₄	—	76	4	no	—
359	C₂×C₄	—	76	4	no	—
360	C₂×C₄	—	76	4	no	—
361	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
362	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
363	C₂×C₄	C₄²×D₁₉	1	2	yes	—
364	C₂×C₄	#10597323	1	1	yes	characteristic
365	C₂×C₄	#10597323	1	2	yes	—
366	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
367	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
368	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
369	C₂×C₄	#10597333	1	1	yes	characteristic
370	C₂×C₄	#10597333	1	2	yes	—
371	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
372	C₂×C₄	#10597338	1	1	yes	characteristic
373	C₂×C₄	#10597338	1	2	yes	—
374	C₂×C₄	#10597339	1	2	yes	—
375	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
376	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
377	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
378	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	38	4	no	—
381	C₂²	#95×D₁₉	1	1	yes	characteristic
382	C₂²	#11926391	1	2	yes	—
383	C₂²	C₂²⋊C₄×Dic₁₉	1	2	yes	—
384	C₂²	#11926395	1	1	yes	characteristic
385	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
386	C₂²	#102×D₁₉	1	2	yes	—
387	C₂²	#103×D₁₉	1	2	yes	—
388	C₂²	#11926537	1	2	yes	—
389	C₂²	#11926539	1	2	yes	—
390	C₂²	#106×D₁₉	1	1	yes	characteristic
391	C₂²	#107×D₁₉	1	1	yes	characteristic
392	C₂²	#11926579	1	1	yes	characteristic
393	C₂²	#11926581	1	1	yes	characteristic
394	C₂²	#11926624	1	2	yes	—
395	C₂²	#11926626	1	1	yes	characteristic
396	C₂²	D₈×Dic₁₉	1	1	yes	characteristic
397	C₂²	#11926629	1	2	yes	—
398	C₂²	#11926631	1	2	yes	—
399	C₂²	SD₁₆×Dic₁₉	1	2	yes	—
400	C₂²	#11926635	1	2	yes	—
401	C₂²	#11926636	1	2	yes	—
402	C₂²	#11926638	1	1	yes	characteristic
403	C₂²	Q₁₆×Dic₁₉	1	1	yes	characteristic
404	C₄	—	4	8	no	—
405	C₄	—	19	8	no	—
406	C₄	—	38	4	no	—
407	C₄	—	76	8	no	—
408	C₄	C₄²×Dic₁₉	1	1	yes	characteristic
409	C₄	#11926389	1	1	yes	characteristic
410	C₄	#11926391	1	1	yes	characteristic
411	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
412	C₄	#11926395	1	2	yes	—
413	C₄	C₄⋊C₄×Dic₁₉	1	2	yes	—
414	C₂	#95×Dic₁₉	1	1	yes	characteristic
415	C₂	D₁₉×#340	1	1	yes	characteristic
416	C₂	#14563350	1	1	yes	characteristic
417	C₂	#14563449	1	2	yes	—
418	C₂	#102×Dic₁₉	1	2	yes	—
419	C₂	#14563454	1	2	yes	—
420	C₂	#103×Dic₁₉	1	2	yes	—
421	C₂	#14563523	1	1	yes	characteristic
422	C₂	#106×Dic₁₉	1	1	yes	characteristic
423	C₂	#14563527	1	1	yes	characteristic
424	C₂	#107×Dic₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₁₉
commutator	C₄×C₁₉	C₄³
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#340	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#340	D₁₉
hypocenter	C₁₉	C₄×#340
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
11. C₂×C₈×Dic₁₉	C₄	semidirect
13. C₄⋊C₄×Dic₁₉	C₄	semidirect
15. #11926307	C₄	semidirect
16. #11926306	C₄	semidirect
19. C₁₉×#340	C₄	semidirect
95. C₂×C₈×C₁₉	C₄²	semidirect
99. C₄⋊C₄×C₁₉	C₄²	semidirect
103. C₄⋊Dic₁₉	C₄²	semidirect
112. C₂×C₁₉⋊C₈	C₄²	semidirect
206. Dic₁₉	#340	direct (N × H)
220. #340	Dic₁₉	direct (N × H)
268. C₁₉	C₄×#340	semidirect
313. C₂×C₈	C₄×Dic₁₉	semidirect
321. C₄⋊C₄	C₄×Dic₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₁₉	2
C₂×C₄⋊C₄×Dic₁₉	2
C₂×#11926307	2
C₂×#11926306	2
C₂×C₁₉×#340	2
C₄×#340	19

Subgroups — #340×Dic19 #18087718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #340×Dic₁₉ #18087718