Subgroups — #18090567

Order 4864.

898 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926306	C₂	1	2	yes	maximal
3	C₂×#11926306	C₂	1	2	yes	maximal
4	#14561865	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	C₂×C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
10	C₂×C₁₉⋊#95	—	2	1	no	—
11	C₂×C₁₉⋊#95	—	2	1	no	—
12	#11926306	—	2	4	no	—
13	#11926306	—	2	4	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	2	no	—
49	C₂×C₄⋊Dic₁₉	Q₈	1	4	yes	—
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	—	2	2	no	—
56	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
57	C₁₉×#95	—	2	4	no	—
58	C₁₉⋊#95	—	4	2	no	—
59	C₁₉⋊#95	—	4	2	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
61	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	4	1	no	—
73	C₂²×C₄×C₁₉	—	4	1	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	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	2	no	—
80	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₁₉	D₈	1	2	yes	—
83	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	2	yes	—
93	C₂²×C₄×C₁₉	#41	1	2	yes	—
94	C₂²×Dic₁₉	—	2	4	no	—
95	C₂²×Dic₁₉	—	4	2	no	—
96	C₂²×Dic₁₉	—	4	2	no	—
97	C₂²×Dic₁₉	—	4	2	no	—
98	C₂²×Dic₁₉	—	4	2	no	—
99	C₂²×Dic₁₉	—	4	2	no	—
100	C₂²×Dic₁₉	—	4	2	no	—
101	C₄⋊C₄×C₁₉	—	2	2	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	—	4	8	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
109	C₄²×C₁₉	—	2	4	no	—
110	C₄²×C₁₉	—	2	2	no	—
111	C₄²×C₁₉	—	2	2	no	—
112	C₄⋊Dic₁₉	—	2	4	no	—
113	C₄⋊Dic₁₉	—	2	4	no	—
114	C₄⋊Dic₁₉	—	4	2	no	—
115	C₄⋊Dic₁₉	—	4	2	no	—
116	C₂×C₁₉⋊C₈	—	2	4	no	—
117	C₂×C₁₉⋊C₈	—	2	4	no	—
118	C₂×C₁₉⋊C₈	—	2	4	no	—
119	C₂×C₁₉⋊C₈	—	4	2	no	—
120	C₂×C₁₉⋊C₈	—	4	2	no	—
121	C₂×C₁₉⋊C₈	—	4	2	no	—
122	C₂×C₁₉⋊C₈	—	4	2	no	—
123	#11227	—	19	1	no	maximal, Sylow
124	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₁₉	#121	1	1	yes	characteristic
126	C₂³×C₁₉	#121	1	2	yes	—
127	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
128	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
129	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
130	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
131	C₂³×C₁₉	#135	1	2	yes	—
132	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
133	C₂³×C₁₉	#137	1	2	yes	—
134	C₂³×C₁₉	#137	1	1	yes	characteristic
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	4	no	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	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	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	8	2	no	—
155	C₂×C₄×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	#102	1	4	yes	—
157	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
161	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#121	1	2	yes	—
164	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#123	1	2	yes	—
169	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#125	1	2	yes	—
171	C₂×C₄×C₁₉	#125	1	2	yes	—
172	C₂×C₄×C₁₉	#126	1	2	yes	—
173	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
175	C₂×Dic₁₉	—	4	4	no	—
176	C₂×Dic₁₉	—	4	4	no	—
177	C₂×Dic₁₉	—	4	4	no	—
178	C₂×Dic₁₉	—	8	2	no	—
179	C₂×Dic₁₉	—	8	2	no	—
180	C₂×Dic₁₉	—	8	2	no	—
181	C₂×Dic₁₉	—	8	2	no	—
182	C₁₉⋊C₈	—	4	4	no	—
183	C₂²×C₄⋊C₈	—	19	1	no	—
184	C₂×#389	D₁₉	1	1	yes	characteristic
185	C₂×#340	—	19	2	no	—
186	C₂×#340	—	19	2	no	—
187	C₄⋊#95	—	19	1	no	—
188	C₂²×C₁₉	#380	1	1	yes	characteristic
189	C₂²×C₁₉	#386	1	1	yes	characteristic
190	C₂²×C₁₉	#391	1	1	yes	characteristic
191	C₂²×C₁₉	#396	1	2	yes	—
192	C₂²×C₁₉	#398	1	2	yes	—
193	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
194	C₂²×C₁₉	#416	1	1	yes	characteristic
195	C₂²×C₁₉	#417	1	1	yes	characteristic
196	C₂²×C₁₉	#419	1	1	yes	characteristic
197	C₂²×C₁₉	#459	1	1	yes	characteristic
198	C₂²×C₁₉	#461	1	1	yes	characteristic
199	C₂²×C₁₉	#464	1	2	yes	—
200	C₂²×C₁₉	#465	1	2	yes	—
201	C₂²×C₁₉	#466	1	2	yes	—
202	C₂²×C₁₉	#468	1	2	yes	—
203	C₂²×C₁₉	#470	1	2	yes	—
204	C₂²×C₁₉	#474	1	2	yes	—
205	C₂²×C₁₉	#474	1	1	yes	characteristic
206	C₂²×C₁₉	#475	1	2	yes	—
207	C₂²×C₁₉	#476	1	1	yes	characteristic
208	C₂²×C₁₉	#478	1	2	yes	—
209	C₂²×C₁₉	#479	1	2	yes	—
210	C₂²×C₁₉	#479	1	2	yes	—
211	C₄×C₁₉	—	2	4	no	—
212	C₄×C₁₉	—	4	4	no	—
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	8	2	no	—
215	C₄×C₁₉	#387	1	2	yes	—
216	C₄×C₁₉	#389	1	2	yes	—
217	C₄×C₁₉	#394	1	1	yes	characteristic
218	C₄×C₁₉	#395	1	1	yes	characteristic
219	C₄×C₁₉	#398	1	1	yes	characteristic
220	C₄×C₁₉	#400	1	1	yes	characteristic
221	Dic₁₉	—	8	4	no	—
222	C₂³×C₈	—	19	2	no	—
223	C₂²×C₄⋊C₄	—	2	1	no	—
224	C₂²×C₄⋊C₄	—	19	2	no	—
225	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
227	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
228	C₂×C₄⋊C₈	—	38	4	no	—
229	C₂×C₄⋊C₈	—	38	2	no	—
230	#389	—	2	2	no	—
231	#389	Dic₁₉	1	4	yes	complemented
232	C₂×#95	—	2	1	no	—
233	C₂×#95	—	38	1	no	—
234	C₂×#95	—	38	1	no	—
235	#340	—	38	4	no	—
236	#340	—	38	4	no	—
237	C₂×C₁₉	#1441	1	1	yes	characteristic
238	C₂×C₁₉	#1802	1	1	yes	characteristic
239	C₂×C₁₉	#1805	1	1	yes	characteristic
240	C₂×C₁₉	#1893	1	1	yes	characteristic
241	C₂×C₁₉	#1894	1	1	yes	characteristic
242	C₂×C₁₉	#1988	1	1	yes	characteristic
243	C₂×C₁₉	#1989	1	1	yes	characteristic
244	C₂×C₁₉	#2066	1	2	yes	—
245	C₂×C₁₉	#2067	1	2	yes	—
246	C₂×C₁₉	#2086	1	2	yes	—
247	C₂×C₁₉	#2088	1	2	yes	—
248	C₂³×C₄	—	2	1	no	—
249	C₂³×C₄	—	2	1	no	—
250	C₂³×C₄	—	38	2	no	—
251	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
252	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
253	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
254	C₂²×C₈	—	19	4	no	—
255	C₂²×C₈	—	38	2	no	—
256	C₂²×C₈	—	38	2	no	—
257	C₂²×C₈	—	38	2	no	—
258	C₂²×C₈	—	38	2	no	—
259	C₂²×C₈	—	38	2	no	—
260	C₂²×C₈	—	38	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	4	2	no	—
269	C₂×C₄⋊C₄	—	4	2	no	—
270	C₂×C₄⋊C₄	—	19	4	no	—
271	C₂×C₄⋊C₄	—	38	2	no	—
272	C₂×C₄⋊C₄	—	38	2	no	—
273	C₂×C₄⋊C₄	—	38	2	no	—
274	C₂×C₄⋊C₄	—	38	2	no	—
275	C₂×C₄⋊C₄	—	38	2	no	—
276	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
277	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
278	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
279	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
283	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
284	C₄⋊C₈	—	38	8	no	—
285	#95	—	2	4	no	—
286	#95	—	76	2	no	—
287	#95	—	76	2	no	—
288	C₁₉	#11227	1	1	yes	characteristic, complemented, Sylow
289	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	38	4	no	—
309	C₂²×C₄	—	76	2	no	—
310	C₂²×C₄	—	76	2	no	—
311	C₂²×C₄	—	76	2	no	—
312	C₂²×C₄	—	76	2	no	—
313	C₂²×C₄	—	76	2	no	—
314	C₂²×C₄	—	76	2	no	—
315	C₂²×C₄	#64525	1	2	yes	—
316	C₂²×C₄	#64526	1	2	yes	—
317	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
318	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
319	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
321	C₂²×C₄	#64541	1	1	yes	characteristic
322	C₂²×C₄	#64541	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₁₉	1	2	yes	—
324	C₂²×C₄	#64543	1	2	yes	—
325	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
326	C₂²×C₄	#64545	1	2	yes	—
327	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
329	C₂×C₈	—	38	4	no	—
330	C₂×C₈	—	38	4	no	—
331	C₂×C₈	—	38	4	no	—
332	C₂×C₈	—	76	2	no	—
333	C₂×C₈	—	76	2	no	—
334	C₂×C₈	—	76	2	no	—
335	C₂×C₈	—	76	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	8	no	—
343	C₄⋊C₄	—	38	4	no	—
344	C₄⋊C₄	—	38	4	no	—
345	C₄⋊C₄	—	76	2	no	—
346	C₄⋊C₄	—	76	2	no	—
347	C₄⋊C₄	C₄⋊Dic₁₉	1	4	yes	—
348	C₄²	—	2	4	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₂³	#10597370	1	1	yes	characteristic
352	C₂³	#10597376	1	1	yes	characteristic
353	C₂³	C₂×#64525	1	1	yes	characteristic
354	C₂³	C₂×#64526	1	1	yes	characteristic
355	C₂³	#10597385	1	2	yes	—
356	C₂³	#10597388	1	2	yes	—
357	C₂³	#10597392	1	2	yes	—
358	C₂³	#10597395	1	1	yes	characteristic
359	C₂³	#10597396	1	2	yes	—
360	C₂³	#10597397	1	1	yes	characteristic
361	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	76	4	no	—
384	C₂×C₄	—	76	4	no	—
385	C₂×C₄	—	76	4	no	—
386	C₂×C₄	—	152	2	no	—
387	C₂×C₄	—	152	2	no	—
388	C₂×C₄	—	152	2	no	—
389	C₂×C₄	—	152	2	no	—
390	C₂×C₄	#10597289	1	4	yes	—
391	C₂×C₄	#10597334	1	2	yes	—
392	C₂×C₄	#10597335	1	2	yes	—
393	C₂×C₄	#10597336	1	2	yes	—
394	C₂×C₄	#10597340	1	2	yes	—
395	C₂×C₄	#10597341	1	2	yes	—
396	C₂×C₄	#10597342	1	2	yes	—
397	C₂×C₄	#10597343	1	2	yes	—
398	C₂×C₄	#10597344	1	2	yes	—
399	C₂×C₄	#10597370	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
401	C₂×C₄	#10597372	1	1	yes	characteristic
402	C₂×C₄	#10597376	1	1	yes	characteristic
403	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
404	C₂×C₄	#10597381	1	1	yes	characteristic
405	C₂×C₄	#10597383	1	1	yes	characteristic
406	C₂×C₄	#10597390	1	1	yes	characteristic
407	C₂×C₄	Q₈×Dic₁₉	1	2	yes	—
408	C₂×C₄	#10597393	1	1	yes	characteristic
409	C₈	—	76	4	no	—
410	C₂²	#11926404	1	1	yes	characteristic
411	C₂²	#11926424	1	1	yes	characteristic
412	C₂²	#11926451	1	1	yes	characteristic
413	C₂²	#11926466	1	2	yes	—
414	C₂²	#11926477	1	2	yes	—
415	C₂²	C₂×#10597289	1	1	yes	characteristic
416	C₂²	#11926540	1	1	yes	characteristic
417	C₂²	#11926545	1	1	yes	characteristic
418	C₂²	#11926553	1	1	yes	characteristic
419	C₂²	#11926739	1	1	yes	characteristic
420	C₂²	#11926749	1	1	yes	characteristic
421	C₂²	#11926766	1	2	yes	—
422	C₂²	#11926771	1	2	yes	—
423	C₂²	#11926778	1	2	yes	—
424	C₂²	#11926792	1	2	yes	—
425	C₂²	#11926800	1	2	yes	—
426	C₂²	#11926821	1	2	yes	—
427	C₂²	#11926824	1	1	yes	characteristic
428	C₂²	#11926826	1	2	yes	—
429	C₂²	#11926834	1	1	yes	characteristic
430	C₂²	#11926841	1	2	yes	—
431	C₂²	#11926848	1	2	yes	—
432	C₂²	#11926851	1	2	yes	—
433	C₄	—	2	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	2	no	—
437	C₄	—	152	4	no	—
438	C₄	#11926430	1	2	yes	—
439	C₄	#11926443	1	2	yes	—
440	C₄	#11926461	1	1	yes	characteristic
441	C₄	#11926464	1	1	yes	characteristic
442	C₄	#11926474	1	1	yes	characteristic
443	C₄	#11926483	1	1	yes	characteristic
444	C₂	#14561888	1	1	yes	characteristic
445	C₂	#14563635	1	1	yes	characteristic
446	C₂	#14563650	1	1	yes	characteristic
447	C₂	#14564064	1	1	yes	characteristic
448	C₂	#14564069	1	1	yes	characteristic
449	C₂	#14564588	1	1	yes	characteristic
450	C₂	#14564593	1	1	yes	characteristic
451	C₂	#14565013	1	2	yes	—
452	C₂	#14565020	1	2	yes	—
453	C₂	#14565126	1	2	yes	—
454	C₂	#14565136	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	#11227
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
231. #389	Dic₁₉	semidirect
288. C₁₉	#11227	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₁₉⋊C₈)	2
C₂×#11926306	2
#14561865	2
C₂×C₁₉×#389	2
#11227	19