Subgroups — #18090449

Order 4864.

958 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926414	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926306	C₂	1	2	yes	maximal
3	C₂×#11926306	C₂	1	2	yes	maximal
4	C₂×#11926299	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
8	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
9	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	#11926414	—	2	4	no	—
11	#11926306	—	2	4	no	—
12	#11926306	—	2	4	no	—
13	#11926299	—	2	2	no	—
14	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#389	—	2	2	no	—
19	C₁₉×#389	C₄	1	4	yes	complemented
20	C₂×C₁₉×#95	—	2	1	no	—
21	C₂³×C₄×C₁₉	—	2	1	no	—
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂³×Dic₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
40	C₂×C₄²×C₁₉	—	2	2	no	—
41	C₂×C₄²×C₁₉	—	2	2	no	—
42	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₁₉	D₄	1	2	yes	—
44	C₂×C₄⋊Dic₁₉	—	2	2	no	—
45	C₂×C₄⋊Dic₁₉	—	2	2	no	—
46	C₂×C₄⋊Dic₁₉	—	2	2	no	—
47	C₂×C₄⋊Dic₁₉	—	2	2	no	—
48	C₂×C₄⋊Dic₁₉	—	2	4	no	—
49	C₂×C₄⋊Dic₁₉	—	2	4	no	—
50	C₂×C₄⋊Dic₁₉	—	2	2	no	—
51	C₂×C₄⋊Dic₁₉	—	4	2	no	—
52	C₂×C₄⋊Dic₁₉	—	4	2	no	—
53	C₂×C₄⋊Dic₁₉	—	4	2	no	—
54	C₂×C₄⋊Dic₁₉	—	4	2	no	—
55	C₂×C₄⋊Dic₁₉	D₄	1	4	yes	—
56	C₂²×C₁₉⋊C₈	—	2	2	no	—
57	C₂²×C₁₉⋊C₈	—	2	2	no	—
58	C₂²×C₁₉⋊C₈	—	2	2	no	—
59	C₂²×C₁₉⋊C₈	—	2	2	no	—
60	C₂²×C₁₉⋊C₈	—	2	2	no	—
61	C₂²×C₁₉⋊C₈	—	2	2	no	—
62	C₂²×C₁₉⋊C₈	Q₈	1	4	yes	—
63	C₁₉×#95	—	2	4	no	—
64	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	4	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	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₁₉	D₈	1	2	yes	—
90	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
91	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	2	yes	—
102	C₂²×C₄×C₁₉	#41	1	2	yes	—
103	C₂²×Dic₁₉	—	2	4	no	—
104	C₂²×Dic₁₉	—	4	2	no	—
105	C₂²×Dic₁₉	—	4	2	no	—
106	C₂²×Dic₁₉	—	4	2	no	—
107	C₂²×Dic₁₉	—	4	2	no	—
108	C₂²×Dic₁₉	—	4	2	no	—
109	C₂²×Dic₁₉	—	4	2	no	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	4	8	no	—
115	C₄⋊C₄×C₁₉	—	4	2	no	—
116	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	complemented
117	C₄²×C₁₉	—	2	4	no	—
118	C₄²×C₁₉	—	2	4	no	—
119	C₄⋊Dic₁₉	—	2	4	no	—
120	C₄⋊Dic₁₉	—	2	4	no	—
121	C₄⋊Dic₁₉	—	4	8	no	—
122	C₄⋊Dic₁₉	—	4	8	no	—
123	C₄⋊Dic₁₉	—	4	2	no	—
124	C₄⋊Dic₁₉	—	4	2	no	—
125	C₂×C₁₉⋊C₈	—	2	4	no	—
126	C₂×C₁₉⋊C₈	—	2	4	no	—
127	C₂×C₁₉⋊C₈	—	2	4	no	—
128	C₂×C₁₉⋊C₈	—	4	2	no	—
129	C₂×C₁₉⋊C₈	—	4	2	no	—
130	C₂×C₁₉⋊C₈	—	4	2	no	—
131	C₂×C₁₉⋊C₈	—	4	2	no	—
132	#11207	—	19	1	no	maximal, Sylow
133	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₁₉	#120	1	1	yes	characteristic
135	C₂³×C₁₉	#121	1	1	yes	characteristic
136	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
137	C₂³×C₁₉	#123	1	1	yes	characteristic
138	C₂³×C₁₉	#124	1	1	yes	characteristic
139	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
140	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
141	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
142	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
143	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
144	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂³×C₁₉	#137	1	1	yes	characteristic
147	C₂³×C₁₉	#137	1	1	yes	characteristic
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	#102	1	4	yes	—
175	C₂×C₄×C₁₉	#103	1	4	yes	—
176	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	2	yes	—
182	C₂×C₄×C₁₉	#121	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	1	yes	characteristic
187	C₂×C₄×C₁₉	#123	1	2	yes	—
188	C₂×C₄×C₁₉	#125	1	2	yes	—
189	C₂×C₄×C₁₉	#125	1	2	yes	—
190	C₂×C₄×C₁₉	#126	1	2	yes	—
191	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
192	C₂×Dic₁₉	—	4	4	no	—
193	C₂×Dic₁₉	—	4	4	no	—
194	C₂×Dic₁₉	—	4	4	no	—
195	C₂×Dic₁₉	—	8	2	no	—
196	C₂×Dic₁₉	—	8	2	no	—
197	C₂×Dic₁₉	—	8	2	no	—
198	C₂×Dic₁₉	—	8	2	no	—
199	C₁₉⋊C₈	—	4	4	no	—
200	C₂×#389	D₁₉	1	1	yes	characteristic
201	C₂×#384	—	19	1	no	—
202	C₂×#340	—	19	2	no	—
203	C₂×#340	—	19	2	no	—
204	C₂×#336	—	19	1	no	—
205	C₂²×C₁₉	#380	1	1	yes	characteristic
206	C₂²×C₁₉	#386	1	1	yes	characteristic
207	C₂²×C₁₉	#391	1	1	yes	characteristic
208	C₂²×C₁₉	#394	1	1	yes	characteristic
209	C₂²×C₁₉	#395	1	1	yes	characteristic
210	C₂²×C₁₉	#398	1	1	yes	characteristic
211	C₂²×C₁₉	#400	1	1	yes	characteristic
212	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
213	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
214	C₂²×C₁₉	#417	1	1	yes	characteristic
215	C₂²×C₁₉	#417	1	1	yes	characteristic
216	C₂²×C₁₉	#447	1	1	yes	characteristic
217	C₂²×C₁₉	#448	1	1	yes	characteristic
218	C₂²×C₁₉	#450	1	1	yes	characteristic
219	C₂²×C₁₉	#451	1	1	yes	characteristic
220	C₂²×C₁₉	#459	1	1	yes	characteristic
221	C₂²×C₁₉	#460	1	1	yes	characteristic
222	C₂²×C₁₉	#461	1	1	yes	characteristic
223	C₂²×C₁₉	#462	1	1	yes	characteristic
224	C₂²×C₁₉	#474	1	1	yes	characteristic
225	C₂²×C₁₉	#475	1	1	yes	characteristic
226	C₂²×C₁₉	#476	1	1	yes	characteristic
227	C₂²×C₁₉	#477	1	1	yes	characteristic
228	C₂²×C₁₉	#480	1	1	yes	characteristic
229	C₂²×C₁₉	#481	1	1	yes	characteristic
230	C₂²×C₁₉	#483	1	1	yes	characteristic
231	C₂²×C₁₉	#484	1	1	yes	characteristic
232	C₂²×C₁₉	#486	1	1	yes	characteristic
233	C₂²×C₁₉	#487	1	1	yes	characteristic
234	C₂²×C₁₉	#490	1	1	yes	characteristic
235	C₂²×C₁₉	#491	1	1	yes	characteristic
236	C₂²×C₁₉	#498	1	1	yes	characteristic
237	C₂²×C₁₉	#500	1	1	yes	characteristic
238	C₂²×C₁₉	#501	1	1	yes	characteristic
239	C₂²×C₁₉	#501	1	1	yes	characteristic
240	C₄×C₁₉	—	2	4	no	—
241	C₄×C₁₉	—	2	4	no	—
242	C₄×C₁₉	—	4	4	no	—
243	C₄×C₁₉	—	8	2	no	—
244	C₄×C₁₉	#387	1	2	yes	—
245	C₄×C₁₉	#389	1	2	yes	—
246	C₄×C₁₉	#396	1	2	yes	—
247	C₄×C₁₉	#398	1	2	yes	—
248	Dic₁₉	—	8	4	no	—
249	C₂³×C₈	—	19	2	no	—
250	C₂²×C₄⋊C₄	—	2	1	no	—
251	C₂²×C₄⋊C₄	—	19	2	no	—
252	C₂²×C₄⋊C₄	—	38	1	no	—
253	C₂²×C₄⋊C₄	—	38	1	no	—
254	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
256	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
257	#389	—	2	2	no	—
258	#389	Dic₁₉	1	4	yes	complemented
259	#384	—	38	4	no	—
260	C₂×#95	—	2	1	no	—
261	#340	—	38	4	no	—
262	#340	—	38	4	no	—
263	#336	—	38	2	no	—
264	C₂×C₁₉	#1441	1	1	yes	characteristic
265	C₂×C₁₉	#1802	1	1	yes	characteristic
266	C₂×C₁₉	#1803	1	1	yes	characteristic
267	C₂×C₁₉	#1872	1	1	yes	characteristic
268	C₂×C₁₉	#1874	1	1	yes	characteristic
269	C₂×C₁₉	#1990	1	1	yes	characteristic
270	C₂×C₁₉	#1992	1	1	yes	characteristic
271	C₂×C₁₉	#2041	1	1	yes	characteristic
272	C₂×C₁₉	#2043	1	1	yes	characteristic
273	C₂×C₁₉	#2057	1	1	yes	characteristic
274	C₂×C₁₉	#2058	1	1	yes	characteristic
275	C₂×C₁₉	#2083	1	1	yes	characteristic
276	C₂×C₁₉	#2084	1	1	yes	characteristic
277	C₂×C₁₉	#2099	1	1	yes	characteristic
278	C₂×C₁₉	#2100	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	—	2	1	no	—
281	C₂³×C₄	—	38	2	no	—
282	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
283	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
284	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
285	C₂²×C₈	—	19	4	no	—
286	C₂²×C₈	—	38	2	no	—
287	C₂²×C₈	—	38	2	no	—
288	C₂²×C₈	—	38	2	no	—
289	C₂²×C₈	—	38	2	no	—
290	C₂²×C₈	—	38	2	no	—
291	C₂²×C₈	—	38	2	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	4	2	no	—
300	C₂×C₄⋊C₄	—	4	2	no	—
301	C₂×C₄⋊C₄	—	19	4	no	—
302	C₂×C₄⋊C₄	—	38	2	no	—
303	C₂×C₄⋊C₄	—	38	2	no	—
304	C₂×C₄⋊C₄	—	38	2	no	—
305	C₂×C₄⋊C₄	—	38	2	no	—
306	C₂×C₄⋊C₄	—	38	4	no	—
307	C₂×C₄⋊C₄	—	38	4	no	—
308	C₂×C₄⋊C₄	—	38	2	no	—
309	C₂×C₄⋊C₄	—	76	2	no	—
310	C₂×C₄⋊C₄	—	76	2	no	—
311	C₂×C₄⋊C₄	—	76	2	no	—
312	C₂×C₄⋊C₄	—	76	2	no	—
313	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
314	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
315	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
320	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
321	#95	—	2	4	no	—
322	C₁₉	#11207	1	1	yes	characteristic, complemented, Sylow
323	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	38	4	no	—
347	C₂²×C₄	—	76	2	no	—
348	C₂²×C₄	—	76	2	no	—
349	C₂²×C₄	—	76	2	no	—
350	C₂²×C₄	—	76	2	no	—
351	C₂²×C₄	—	76	2	no	—
352	C₂²×C₄	—	76	2	no	—
353	C₂²×C₄	#64525	1	2	yes	—
354	C₂²×C₄	#64526	1	2	yes	—
355	C₂²×C₄	#64527	1	2	yes	—
356	C₂²×C₄	#64528	1	2	yes	—
357	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
358	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
359	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
361	C₂²×C₄	#64541	1	1	yes	characteristic
362	C₂²×C₄	#64541	1	1	yes	characteristic
363	C₂²×C₄	D₄×D₁₉	1	2	yes	—
364	C₂²×C₄	#64543	1	2	yes	—
365	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
366	C₂²×C₄	#64545	1	2	yes	—
367	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
369	C₂×C₈	—	38	4	no	—
370	C₂×C₈	—	38	4	no	—
371	C₂×C₈	—	38	4	no	—
372	C₂×C₈	—	76	2	no	—
373	C₂×C₈	—	76	2	no	—
374	C₂×C₈	—	76	2	no	—
375	C₂×C₈	—	76	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	8	no	—
382	C₄⋊C₄	—	38	4	no	—
383	C₄⋊C₄	—	38	4	no	—
384	C₄⋊C₄	—	76	8	no	—
385	C₄⋊C₄	—	76	8	no	—
386	C₄⋊C₄	—	76	2	no	—
387	C₄⋊C₄	—	76	2	no	—
388	C₄⋊C₄	C₄⋊Dic₁₉	1	4	yes	complemented
389	C₄²	—	2	4	no	—
390	C₄²	—	2	4	no	—
391	C₂³	#10597370	1	1	yes	characteristic
392	C₂³	#10597376	1	1	yes	characteristic
393	C₂³	C₂×#64525	1	1	yes	characteristic
394	C₂³	C₂×#64526	1	1	yes	characteristic
395	C₂³	#10597381	1	1	yes	characteristic
396	C₂³	#10597383	1	1	yes	characteristic
397	C₂³	C₂×#64527	1	1	yes	characteristic
398	C₂³	C₂×#64528	1	1	yes	characteristic
399	C₂³	#10597390	1	1	yes	characteristic
400	C₂³	#10597393	1	1	yes	characteristic
401	C₂³	#10597395	1	1	yes	characteristic
402	C₂³	#10597395	1	1	yes	characteristic
403	C₂³	#10597397	1	1	yes	characteristic
404	C₂³	#10597397	1	1	yes	characteristic
405	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	1	no	—
429	C₂×C₄	—	8	1	no	—
430	C₂×C₄	—	8	1	no	—
431	C₂×C₄	—	8	1	no	—
432	C₂×C₄	—	76	4	no	—
433	C₂×C₄	—	76	4	no	—
434	C₂×C₄	—	76	4	no	—
435	C₂×C₄	—	152	2	no	—
436	C₂×C₄	—	152	2	no	—
437	C₂×C₄	—	152	2	no	—
438	C₂×C₄	—	152	2	no	—
439	C₂×C₄	#10597289	1	4	yes	—
440	C₂×C₄	#10597292	1	4	yes	—
441	C₂×C₄	#10597334	1	2	yes	—
442	C₂×C₄	#10597335	1	2	yes	—
443	C₂×C₄	#10597336	1	2	yes	—
444	C₂×C₄	#10597340	1	2	yes	—
445	C₂×C₄	#10597341	1	2	yes	—
446	C₂×C₄	#10597342	1	2	yes	—
447	C₂×C₄	#10597343	1	2	yes	—
448	C₂×C₄	#10597344	1	2	yes	—
449	C₂×C₄	#10597370	1	1	yes	characteristic
450	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
451	C₂×C₄	#10597372	1	1	yes	characteristic
452	C₂×C₄	#10597376	1	1	yes	characteristic
453	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
454	C₂×C₄	#10597385	1	2	yes	—
455	C₂×C₄	Q₈×Dic₁₉	1	2	yes	—
456	C₂×C₄	#10597392	1	2	yes	—
457	C₈	—	76	4	no	—
458	C₂²	#11926404	1	1	yes	characteristic
459	C₂²	#11926424	1	1	yes	characteristic
460	C₂²	#11926451	1	1	yes	characteristic
461	C₂²	#11926461	1	1	yes	characteristic
462	C₂²	#11926464	1	1	yes	characteristic
463	C₂²	#11926474	1	1	yes	characteristic
464	C₂²	#11926483	1	1	yes	characteristic
465	C₂²	C₂×#10597289	1	1	yes	characteristic
466	C₂²	C₂×#10597292	1	1	yes	characteristic
467	C₂²	#11926545	1	1	yes	characteristic
468	C₂²	#11926545	1	1	yes	characteristic
469	C₂²	#11926677	1	1	yes	characteristic
470	C₂²	#11926682	1	1	yes	characteristic
471	C₂²	#11926694	1	1	yes	characteristic
472	C₂²	#11926699	1	1	yes	characteristic
473	C₂²	#11926739	1	1	yes	characteristic
474	C₂²	#11926744	1	1	yes	characteristic
475	C₂²	#11926749	1	1	yes	characteristic
476	C₂²	#11926754	1	1	yes	characteristic
477	C₂²	#11926824	1	1	yes	characteristic
478	C₂²	#11926829	1	1	yes	characteristic
479	C₂²	#11926834	1	1	yes	characteristic
480	C₂²	#11926839	1	1	yes	characteristic
481	C₂²	#11926855	1	1	yes	characteristic
482	C₂²	#11926860	1	1	yes	characteristic
483	C₂²	#11926872	1	1	yes	characteristic
484	C₂²	#11926877	1	1	yes	characteristic
485	C₂²	#11926892	1	1	yes	characteristic
486	C₂²	#11926896	1	1	yes	characteristic
487	C₂²	#11926910	1	1	yes	characteristic
488	C₂²	#11926914	1	1	yes	characteristic
489	C₂²	#11926940	1	1	yes	characteristic
490	C₂²	#11926947	1	1	yes	characteristic
491	C₂²	#11926954	1	1	yes	characteristic
492	C₂²	#11926954	1	1	yes	characteristic
493	C₄	—	2	4	no	—
494	C₄	—	2	4	no	—
495	C₄	—	4	4	no	—
496	C₄	—	8	2	no	—
497	C₄	—	152	4	no	—
498	C₄	#11926430	1	2	yes	—
499	C₄	#11926443	1	2	yes	—
500	C₄	#11926466	1	2	yes	—
501	C₄	#11926477	1	2	yes	—
502	C₂	#14561888	1	1	yes	characteristic
503	C₂	#14563635	1	1	yes	characteristic
504	C₂	#14563640	1	1	yes	characteristic
505	C₂	#14563943	1	1	yes	characteristic
506	C₂	#14563953	1	1	yes	characteristic
507	C₂	#14564597	1	1	yes	characteristic
508	C₂	#14564605	1	1	yes	characteristic
509	C₂	#14564869	1	1	yes	characteristic
510	C₂	#14564881	1	1	yes	characteristic
511	C₂	#14564963	1	1	yes	characteristic
512	C₂	#14564968	1	1	yes	characteristic
513	C₂	#14565106	1	1	yes	characteristic
514	C₂	#14565111	1	1	yes	characteristic
515	C₂	#14565193	1	1	yes	characteristic
516	C₂	#14565198	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#389	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#389	D₁₉
hypocenter	C₁₉	#11207
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#389

Complements

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

N	H ≅ G/N	type
19. C₁₉×#389	C₄	semidirect
116. C₄⋊C₄×C₁₉	C₄⋊C₄	semidirect
258. #389	Dic₁₉	semidirect
322. C₁₉	#11207	semidirect
388. 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
C₂×#11926414	2
C₂×#11926306	2
C₂×#11926299	2
C₂×C₁₉×#389	2
#11207	19