Subgroups — #18090454

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926410	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	C₂²	1	2	yes	—
8	#11926410	—	2	4	no	—
9	C₂×C₁₉⋊#95	—	2	1	no	—
10	C₂×C₁₉⋊#95	—	2	1	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	4	no	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
39	C₂×C₄²×C₁₉	—	2	2	no	—
40	C₂×C₄²×C₁₉	—	2	2	no	—
41	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₁₉	D₄	1	2	yes	—
43	C₂×C₄⋊Dic₁₉	—	2	2	no	—
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	D₄	1	4	yes	—
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	2	no	—
51	C₂²×C₁₉⋊C₈	—	2	2	no	—
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	2	2	no	—
54	C₂²×C₁₉⋊C₈	—	2	2	no	—
55	C₂²×C₁₉⋊C₈	Q₈	1	4	yes	—
56	C₁₉×#95	—	2	4	no	—
57	C₁₉⋊#95	—	2	4	no	—
58	C₁₉⋊#95	—	2	4	no	—
59	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	4	2	no	—
73	C₂²×C₄×C₁₉	—	4	2	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	2	no	—
77	C₂²×C₄×C₁₉	—	4	2	no	—
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	2	yes	—
89	C₂²×C₄×C₁₉	#41	1	2	yes	—
90	C₂²×Dic₁₉	—	2	4	no	—
91	C₂²×Dic₁₉	—	4	2	no	—
92	C₂²×Dic₁₉	—	4	2	no	—
93	C₂²×Dic₁₉	—	4	2	no	—
94	C₂²×Dic₁₉	—	4	2	no	—
95	C₂²×Dic₁₉	—	4	2	no	—
96	C₂²×Dic₁₉	—	4	2	no	—
97	C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	2	4	no	—
101	C₄⋊C₄×C₁₉	—	4	8	no	—
102	C₄⋊C₄×C₁₉	—	4	2	no	—
103	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
104	C₄²×C₁₉	—	2	4	no	—
105	C₄²×C₁₉	—	2	4	no	—
106	C₄⋊Dic₁₉	—	2	4	no	—
107	C₄⋊Dic₁₉	—	2	4	no	—
108	C₄⋊Dic₁₉	—	4	2	no	—
109	C₄⋊Dic₁₉	—	4	2	no	—
110	C₂×C₁₉⋊C₈	—	2	4	no	—
111	C₂×C₁₉⋊C₈	—	2	4	no	—
112	C₂×C₁₉⋊C₈	—	2	4	no	—
113	C₂×C₁₉⋊C₈	—	4	2	no	—
114	C₂×C₁₉⋊C₈	—	4	2	no	—
115	C₂×C₁₉⋊C₈	—	4	2	no	—
116	C₂×C₁₉⋊C₈	—	4	2	no	—
117	#11208	—	19	1	no	maximal, Sylow
118	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₁₉	#120	1	1	yes	characteristic
120	C₂³×C₁₉	#121	1	1	yes	characteristic
121	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
122	C₂³×C₁₉	#123	1	1	yes	characteristic
123	C₂³×C₁₉	#124	1	1	yes	characteristic
124	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
125	C₂³×C₁₉	#135	1	2	yes	—
126	C₂³×C₁₉	#135	1	2	yes	—
127	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
128	C₂³×C₁₉	#137	1	2	yes	—
129	C₂×C₄×C₁₉	—	2	4	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	4	no	—
141	C₂×C₄×C₁₉	—	4	4	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	8	2	no	—
148	C₂×C₄×C₁₉	—	8	2	no	—
149	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
153	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	2	yes	—
155	C₂×C₄×C₁₉	#121	1	2	yes	—
156	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
159	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#123	1	2	yes	—
161	C₂×C₄×C₁₉	#125	1	2	yes	—
162	C₂×C₄×C₁₉	#125	1	2	yes	—
163	C₂×C₄×C₁₉	#126	1	2	yes	—
164	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
165	C₂×Dic₁₉	—	4	4	no	—
166	C₂×Dic₁₉	—	4	4	no	—
167	C₂×Dic₁₉	—	4	4	no	—
168	C₂×Dic₁₉	—	8	2	no	—
169	C₂×Dic₁₉	—	8	2	no	—
170	C₂×Dic₁₉	—	8	2	no	—
171	C₂×Dic₁₉	—	8	2	no	—
172	C₁₉⋊C₈	—	4	4	no	—
173	C₂×#389	D₁₉	1	1	yes	characteristic
174	C₂×#382	—	19	1	no	—
175	C₂×#340	—	19	2	no	—
176	C₂×#340	—	19	2	no	—
177	C₂×#336	—	19	1	no	—
178	C₂²×C₁₉	#380	1	1	yes	characteristic
179	C₂²×C₁₉	#386	1	1	yes	characteristic
180	C₂²×C₁₉	#391	1	1	yes	characteristic
181	C₂²×C₁₉	#394	1	1	yes	characteristic
182	C₂²×C₁₉	#395	1	1	yes	characteristic
183	C₂²×C₁₉	#398	1	1	yes	characteristic
184	C₂²×C₁₉	#400	1	1	yes	characteristic
185	C₂²×C₁₉	#416	1	1	yes	characteristic
186	C₂²×C₁₉	#416	1	1	yes	characteristic
187	C₂²×C₁₉	#418	1	1	yes	characteristic
188	C₂²×C₁₉	#419	1	1	yes	characteristic
189	C₂²×C₁₉	#449	1	2	yes	—
190	C₂²×C₁₉	#452	1	2	yes	—
191	C₂²×C₁₉	#463	1	2	yes	—
192	C₂²×C₁₉	#464	1	2	yes	—
193	C₂²×C₁₉	#478	1	2	yes	—
194	C₂²×C₁₉	#479	1	2	yes	—
195	C₂²×C₁₉	#482	1	2	yes	—
196	C₂²×C₁₉	#485	1	2	yes	—
197	C₂²×C₁₉	#488	1	2	yes	—
198	C₂²×C₁₉	#489	1	2	yes	—
199	C₂²×C₁₉	#499	1	2	yes	—
200	C₂²×C₁₉	#501	1	2	yes	—
201	C₄×C₁₉	—	4	4	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	8	2	no	—
205	C₄×C₁₉	#387	1	2	yes	—
206	C₄×C₁₉	#389	1	2	yes	—
207	C₄×C₁₉	#396	1	2	yes	—
208	C₄×C₁₉	#398	1	2	yes	—
209	Dic₁₉	—	8	4	no	—
210	C₂³×C₈	—	19	2	no	—
211	C₂²×C₄⋊C₄	—	2	1	no	—
212	C₂²×C₄⋊C₄	—	19	2	no	—
213	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
214	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
215	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
216	#389	—	2	2	no	—
217	#389	Dic₁₉	1	4	yes	complemented
218	#382	—	38	4	no	—
219	C₂×#95	—	2	1	no	—
220	C₂×#95	—	38	1	no	—
221	C₂×#95	—	38	1	no	—
222	#340	—	38	4	no	—
223	#340	—	38	4	no	—
224	#336	—	38	2	no	—
225	C₂×C₁₉	#1441	1	1	yes	characteristic
226	C₂×C₁₉	#1804	1	1	yes	characteristic
227	C₂×C₁₉	#1805	1	1	yes	characteristic
228	C₂×C₁₉	#1873	1	1	yes	characteristic
229	C₂×C₁₉	#1875	1	1	yes	characteristic
230	C₂×C₁₉	#1991	1	1	yes	characteristic
231	C₂×C₁₉	#1993	1	1	yes	characteristic
232	C₂×C₁₉	#2042	1	2	yes	—
233	C₂×C₁₉	#2059	1	2	yes	—
234	C₂×C₁₉	#2085	1	2	yes	—
235	C₂×C₁₉	#2101	1	2	yes	—
236	C₂³×C₄	—	2	1	no	—
237	C₂³×C₄	—	2	1	no	—
238	C₂³×C₄	—	38	2	no	—
239	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
240	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
241	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
242	C₂²×C₈	—	19	4	no	—
243	C₂²×C₈	—	38	2	no	—
244	C₂²×C₈	—	38	2	no	—
245	C₂²×C₈	—	38	2	no	—
246	C₂²×C₈	—	38	2	no	—
247	C₂²×C₈	—	38	2	no	—
248	C₂²×C₈	—	38	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	4	4	no	—
257	C₂×C₄⋊C₄	—	19	4	no	—
258	C₂×C₄⋊C₄	—	38	2	no	—
259	C₂×C₄⋊C₄	—	38	2	no	—
260	C₂×C₄⋊C₄	—	38	2	no	—
261	C₂×C₄⋊C₄	—	38	2	no	—
262	C₂×C₄⋊C₄	—	38	2	no	—
263	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
264	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
265	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
266	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
270	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
271	#95	—	2	4	no	—
272	#95	—	38	4	no	—
273	#95	—	38	4	no	—
274	C₁₉	#11208	1	1	yes	characteristic, complemented, Sylow
275	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	38	4	no	—
295	C₂²×C₄	—	76	2	no	—
296	C₂²×C₄	—	76	2	no	—
297	C₂²×C₄	—	76	2	no	—
298	C₂²×C₄	—	76	2	no	—
299	C₂²×C₄	—	76	2	no	—
300	C₂²×C₄	—	76	2	no	—
301	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
302	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
303	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
305	C₂²×C₄	#64541	1	1	yes	characteristic
306	C₂²×C₄	#64541	1	1	yes	characteristic
307	C₂²×C₄	D₄×D₁₉	1	2	yes	—
308	C₂²×C₄	#64543	1	2	yes	—
309	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
310	C₂²×C₄	#64545	1	2	yes	—
311	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
313	C₂×C₈	—	38	4	no	—
314	C₂×C₈	—	38	4	no	—
315	C₂×C₈	—	38	4	no	—
316	C₂×C₈	—	76	2	no	—
317	C₂×C₈	—	76	2	no	—
318	C₂×C₈	—	76	2	no	—
319	C₂×C₈	—	76	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	4	8	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	38	4	no	—
327	C₄⋊C₄	—	38	4	no	—
328	C₄⋊C₄	—	76	2	no	—
329	C₄⋊C₄	—	76	2	no	—
330	C₄⋊C₄	C₄⋊Dic₁₉	1	4	yes	—
331	C₄²	—	2	4	no	—
332	C₄²	—	2	4	no	—
333	C₂³	#10597370	1	1	yes	characteristic
334	C₂³	#10597376	1	1	yes	characteristic
335	C₂³	#10597378	1	2	yes	—
336	C₂³	#10597381	1	1	yes	characteristic
337	C₂³	#10597383	1	1	yes	characteristic
338	C₂³	#10597388	1	2	yes	—
339	C₂³	#10597390	1	1	yes	characteristic
340	C₂³	#10597393	1	1	yes	characteristic
341	C₂³	#10597396	1	2	yes	—
342	C₂³	#10597396	1	2	yes	—
343	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	—	76	4	no	—
365	C₂×C₄	—	76	4	no	—
366	C₂×C₄	—	76	4	no	—
367	C₂×C₄	—	152	2	no	—
368	C₂×C₄	—	152	2	no	—
369	C₂×C₄	—	152	2	no	—
370	C₂×C₄	—	152	2	no	—
371	C₂×C₄	#10597334	1	2	yes	—
372	C₂×C₄	#10597335	1	2	yes	—
373	C₂×C₄	#10597336	1	2	yes	—
374	C₂×C₄	#10597340	1	2	yes	—
375	C₂×C₄	#10597341	1	2	yes	—
376	C₂×C₄	#10597342	1	2	yes	—
377	C₂×C₄	#10597343	1	2	yes	—
378	C₂×C₄	#10597344	1	2	yes	—
379	C₂×C₄	#10597370	1	1	yes	characteristic
380	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
381	C₂×C₄	#10597372	1	1	yes	characteristic
382	C₂×C₄	#10597376	1	1	yes	characteristic
383	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
384	C₂×C₄	#10597385	1	2	yes	—
385	C₂×C₄	Q₈×Dic₁₉	1	2	yes	—
386	C₂×C₄	#10597392	1	2	yes	—
387	C₈	—	76	4	no	—
388	C₂²	#11926404	1	1	yes	characteristic
389	C₂²	#11926424	1	1	yes	characteristic
390	C₂²	#11926451	1	1	yes	characteristic
391	C₂²	#11926461	1	1	yes	characteristic
392	C₂²	#11926464	1	1	yes	characteristic
393	C₂²	#11926474	1	1	yes	characteristic
394	C₂²	#11926483	1	1	yes	characteristic
395	C₂²	#11926540	1	1	yes	characteristic
396	C₂²	#11926540	1	1	yes	characteristic
397	C₂²	#11926549	1	1	yes	characteristic
398	C₂²	#11926553	1	1	yes	characteristic
399	C₂²	#11926687	1	2	yes	—
400	C₂²	#11926704	1	2	yes	—
401	C₂²	#11926759	1	2	yes	—
402	C₂²	#11926766	1	2	yes	—
403	C₂²	#11926844	1	2	yes	—
404	C₂²	#11926851	1	2	yes	—
405	C₂²	#11926865	1	2	yes	—
406	C₂²	#11926882	1	2	yes	—
407	C₂²	#11926901	1	2	yes	—
408	C₂²	#11926906	1	2	yes	—
409	C₂²	#11926943	1	2	yes	—
410	C₂²	#11926950	1	2	yes	—
411	C₄	—	4	4	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	2	no	—
415	C₄	—	152	4	no	—
416	C₄	#11926430	1	2	yes	—
417	C₄	#11926443	1	2	yes	—
418	C₄	#11926466	1	2	yes	—
419	C₄	#11926477	1	2	yes	—
420	C₂	#14561888	1	1	yes	characteristic
421	C₂	#14563645	1	1	yes	characteristic
422	C₂	#14563650	1	1	yes	characteristic
423	C₂	#14563948	1	1	yes	characteristic
424	C₂	#14563958	1	1	yes	characteristic
425	C₂	#14564601	1	1	yes	characteristic
426	C₂	#14564609	1	1	yes	characteristic
427	C₂	#14564876	1	2	yes	—
428	C₂	#14564973	1	2	yes	—
429	C₂	#14565116	1	2	yes	—
430	C₂	#14565203	1	2	yes	—

	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	#11208
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
217. #389	Dic₁₉	semidirect
274. C₁₉	#11208	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926410	2
C₂×#11926306	2
C₂×#11926299	2
C₂×C₁₉×#389	2
#11208	19