Subgroups — #18077901

Order 4864.

670 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64520	C₂	1	1	yes	maximal, characteristic
2	#14563615	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal, complemented
4	#14561476	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	—	2	1	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₄×#64520	—	2	4	no	—
10	C₂×#10597260	—	2	1	no	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
12	#11926299	—	2	1	no	—
13	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
14	C₂×C₁₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#391	C₄	1	1	yes	characteristic
18	C₁₉×#389	C₄	1	1	yes	characteristic
19	C₁₉×#387	—	2	1	no	—
20	C₁₉×#385	—	2	1	no	—
21	C₁₉×#380	C₄	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₁₉×C₂²⋊Q₈	—	2	2	no	—
30	C₁₉×C₂²⋊Q₈	—	2	2	no	—
31	C₄×Q₈×C₁₉	—	2	2	no	—
32	C₄×Q₈×C₁₉	—	2	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	2	no	—
42	C₂×C₄²×C₁₉	—	2	2	no	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×#64520	—	2	4	no	—
50	C₂×#64520	—	2	4	no	—
51	C₂×#64520	—	2	4	no	—
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	2	2	no	—
54	C₁₉×#95	—	2	1	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	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
62	#10597260	—	2	4	no	—
63	C₄×C₁₉⋊C₈	—	2	2	no	—
64	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
65	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×Q₈×C₁₉	—	2	1	no	—
67	C₂×Q₈×C₁₉	—	2	2	no	—
68	C₂×Q₈×C₁₉	—	2	2	no	—
69	C₂×Q₈×C₁₉	M₁₆	1	2	yes	complemented
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₄⋊C₄×C₁₉	—	2	4	no	—
93	C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₄⋊C₄×C₁₉	—	4	2	no	—
97	C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	complemented
100	C₂²⋊C₄×C₁₉	—	2	4	no	—
101	C₂²⋊C₄×C₁₉	—	4	2	no	—
102	C₄²×C₁₉	—	2	2	no	—
103	C₄²×C₁₉	—	2	1	no	—
104	C₄²×C₁₉	—	2	2	no	—
105	C₄²×C₁₉	—	2	1	no	—
106	C₄²×C₁₉	—	4	2	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	—	4	1	no	—
109	C₄²×C₁₉	C₂×D₄	1	2	yes	—
110	C₄²×C₁₉	#41	1	2	yes	—
111	#64520	—	2	16	no	—
112	C₂×C₁₉⋊C₈	—	2	4	no	—
113	C₂×C₁₉⋊C₈	—	2	4	no	—
114	C₂×C₁₉⋊C₈	—	2	4	no	—
115	C₂×C₁₉⋊C₈	—	4	2	no	—
116	C₂×C₁₉⋊C₈	—	4	2	no	—
117	C₂×C₁₉⋊C₈	—	4	2	no	—
118	#9077	—	19	1	no	maximal, Sylow
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	—	2	1	no	—
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	#104	1	2	yes	—
126	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	Q₈×C₁₉	—	2	4	no	—
128	Q₈×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	—	2	4	no	—
130	C₂×C₄×C₁₉	—	2	4	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	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	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	—	2	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	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	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	#104	1	2	yes	—
158	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#121	1	2	yes	—
161	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#131	1	2	yes	—
165	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#137	1	2	yes	—
167	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
168	C₁₉⋊C₈	—	2	8	no	—
169	C₁₉⋊C₈	—	8	2	no	—
170	C₂×C₄×M₁₆	—	19	1	no	—
171	C₄×C₂²⋊Q₈	D₁₉	1	1	yes	characteristic
172	#1797	—	19	1	no	—
173	C₂×Q₈⋊C₈	—	19	2	no	—
174	#1279	—	19	2	no	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	4	1	no	—
179	C₂²×C₁₉	—	4	1	no	—
180	C₂²×C₁₉	—	4	1	no	—
181	C₂²×C₁₉	—	4	1	no	—
182	C₂²×C₁₉	#386	1	1	yes	characteristic
183	C₂²×C₁₉	#407	1	1	yes	characteristic
184	C₂²×C₁₉	#408	1	1	yes	characteristic
185	C₂²×C₁₉	#417	1	1	yes	characteristic
186	C₂²×C₁₉	#419	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
188	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	2	2	no	—
191	C₄×C₁₉	—	2	1	no	—
192	C₄×C₁₉	—	4	1	no	—
193	C₄×C₁₉	—	4	2	no	—
194	C₄×C₁₉	—	4	1	no	—
195	C₄×C₁₉	—	4	2	no	—
196	C₄×C₁₉	—	8	1	no	—
197	C₄×C₁₉	—	8	1	no	—
198	C₄×C₁₉	#435	1	2	yes	—
199	C₄×C₁₉	#436	1	2	yes	—
200	C₄×C₁₉	#468	1	2	yes	—
201	C₄×C₁₉	#470	1	2	yes	—
202	C₂²×M₁₆	—	38	1	no	—
203	C₂×C₂²⋊Q₈	Dic₁₉	1	1	yes	characteristic
204	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
205	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
206	C₂×C₄⋊C₈	—	19	2	no	—
207	C₂×C₂²⋊C₈	—	38	1	no	—
208	C₄×M₁₆	—	38	4	no	—
209	C₂×#97	—	38	1	no	—
210	C₂×C₄×C₈	—	19	2	no	—
211	#391	Dic₁₉	1	1	yes	characteristic
212	#389	Dic₁₉	1	1	yes	characteristic
213	#387	—	2	1	no	—
214	#385	—	2	1	no	—
215	#380	Dic₁₉	1	1	yes	characteristic
216	C₄×C₄⋊C₄	—	2	1	no	—
217	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
218	C₄×C₂²⋊C₄	—	2	1	no	—
219	#336	—	38	1	no	—
220	Q₈⋊C₈	—	38	4	no	—
221	C₂×C₁₉	—	4	2	no	—
222	C₂×C₁₉	#1483	1	1	yes	characteristic
223	C₂×C₁₉	#1485	1	1	yes	characteristic
224	C₂×C₁₉	#1489	1	1	yes	characteristic
225	C₂×C₁₉	#1491	1	1	yes	characteristic
226	C₂×C₁₉	#1870	1	1	yes	characteristic
227	C₂×C₁₉	#1894	1	1	yes	characteristic
228	C₂×C₁₉	#1896	1	1	yes	characteristic
229	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
230	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
231	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
232	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
233	C₂×M₁₆	—	38	4	no	—
234	C₂×M₁₆	—	38	4	no	—
235	C₂×M₁₆	—	38	4	no	—
236	C₂²×C₈	—	38	2	no	—
237	C₂²×C₈	—	38	2	no	—
238	C₂²⋊Q₈	—	2	2	no	—
239	C₂²⋊Q₈	—	2	2	no	—
240	C₄×Q₈	—	2	2	no	—
241	C₄×Q₈	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
255	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
256	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
258	C₄⋊C₈	—	38	2	no	—
259	C₄⋊C₈	—	38	2	no	—
260	C₂²⋊C₈	—	76	2	no	—
261	#97	—	38	4	no	—
262	C₄×C₈	—	19	4	no	—
263	C₄×C₈	—	38	2	no	—
264	#95	—	2	1	no	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	#95	—	2	1	no	—
268	#95	—	2	1	no	—
269	C₁₉	#9077	1	1	yes	characteristic, complemented, Sylow
270	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	#64520	1	2	yes	complemented
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
292	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
297	M₁₆	—	38	16	no	—
298	C₂×C₈	—	38	4	no	—
299	C₂×C₈	—	38	4	no	—
300	C₂×C₈	—	38	4	no	—
301	C₂×C₈	—	76	2	no	—
302	C₂×C₈	—	76	2	no	—
303	C₂×C₈	—	76	2	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	#64520	1	2	yes	complemented
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	4	2	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	4	1	no	—
321	C₄²	D₄×D₁₉	1	2	yes	—
322	C₄²	#64543	1	2	yes	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	#10597294	1	2	yes	—
330	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
331	Q₈	—	2	4	no	—
332	Q₈	—	4	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	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	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	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	#10597294	1	2	yes	—
362	C₂×C₄	C₂×#64520	1	1	yes	characteristic
363	C₂×C₄	C₂×#64520	1	1	yes	characteristic
364	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
365	C₂×C₄	#10597381	1	1	yes	characteristic
366	C₂×C₄	#10597383	1	1	yes	characteristic
367	C₂×C₄	#10597385	1	2	yes	—
368	C₂×C₄	#10597388	1	2	yes	—
369	C₂×C₄	#10597394	1	2	yes	—
370	C₂×C₄	#10597395	1	1	yes	characteristic
371	C₂×C₄	#10597397	1	1	yes	characteristic
372	C₈	—	38	8	no	—
373	C₈	—	152	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	#11926424	1	1	yes	characteristic
382	C₂²	#11926508	1	1	yes	characteristic
383	C₂²	#11926511	1	1	yes	characteristic
384	C₂²	#11926545	1	1	yes	characteristic
385	C₂²	#11926553	1	1	yes	characteristic
386	C₂²	C₂×#10597294	1	1	yes	characteristic
387	C₂²	C₂×#10597294	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	1	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	1	no	—
397	C₄	#11926616	1	2	yes	—
398	C₄	#11926622	1	2	yes	—
399	C₄	#11926792	1	2	yes	—
400	C₄	#11926800	1	2	yes	—
401	C₂	—	4	2	no	—
402	C₂	#14562048	1	1	yes	characteristic
403	C₂	#14562056	1	1	yes	characteristic
404	C₂	#14562074	1	1	yes	characteristic
405	C₂	#14562082	1	1	yes	characteristic
406	C₂	#14563933	1	1	yes	characteristic
407	C₂	#14564069	1	1	yes	characteristic
408	C₂	#14564079	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×C₂²⋊Q₈	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₁₉
hypocenter	C₁₉	#9077
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
4. #14561476	C₂	semidirect
69. C₂×Q₈×C₁₉	M₁₆	semidirect
99. C₄⋊C₄×C₁₉	M₁₆	semidirect
269. C₁₉	#9077	semidirect
274. C₂×Q₈	#64520	semidirect
311. C₄⋊C₄	#64520	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#64520	2
#14563615	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
#14561476	2
C₄×C₁₉×C₂²⋊Q₈	2
#9077	19