Subgroups — #18075226

Order 4864.

588 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597333	C₂	1	1	yes	maximal, characteristic
2	#14563786	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926276	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926274	C₂	1	1	yes	maximal, characteristic
6	#14561476	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂×#10597333	C₄	1	1	yes	characteristic
10	C₂×#10597333	C₄	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₉⋊C₈	—	2	1	no	—
13	C₂×Dic₁₉⋊C₈	—	2	1	no	—
14	C₂×Dic₁₉⋊C₈	—	2	1	no	—
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×Dic₁₉	C₄	1	1	yes	characteristic
17	C₄⋊C₄×Dic₁₉	C₄	1	1	yes	characteristic
18	C₄×Dic₁₉⋊C₄	—	2	1	no	—
19	#11926395	—	2	1	no	—
20	#11926395	—	2	1	no	—
21	C₄²×Dic₁₉	—	2	1	no	—
22	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
23	#11926298	—	2	1	no	—
24	#11926276	—	2	2	no	—
25	#11926274	—	2	2	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×Dic₁₉⋊C₄	—	2	1	no	—
38	C₂×Dic₁₉⋊C₄	—	2	1	no	—
39	C₂×Dic₁₉⋊C₄	—	2	1	no	—
40	C₂×C₄×Dic₁₉	—	2	1	no	—
41	C₂×C₄×Dic₁₉	—	2	1	no	—
42	C₂×C₄×Dic₁₉	—	2	1	no	—
43	C₂×C₄×Dic₁₉	—	2	1	no	—
44	C₂×C₄×Dic₁₉	—	2	1	no	—
45	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	#10597333	—	2	2	no	—
54	#10597333	—	2	2	no	—
55	#10597333	—	2	2	no	—
56	#10597333	C₈	1	4	yes	complemented
57	C₄×Dic₃₈	—	2	1	no	—
58	C₄×Dic₃₈	—	2	1	no	—
59	C₄×Dic₃₈	D₄	1	2	yes	—
60	C₄×Dic₃₈	Q₈	1	2	yes	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₄×C₈×C₁₉	—	2	1	no	—
64	C₄×C₈×C₁₉	—	2	1	no	—
65	C₁₉×#95	—	2	1	no	—
66	C₁₉⋊#95	—	2	1	no	—
67	C₁₉⋊#95	—	2	1	no	—
68	Dic₁₉⋊C₈	—	2	4	no	—
69	Dic₁₉⋊C₈	—	4	2	no	—
70	Dic₁₉⋊C₈	—	4	2	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄×C₁₉⋊C₈	—	2	1	no	—
74	C₄×C₁₉⋊C₈	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₁₉	—	2	1	no	—
81	C₂²×Dic₁₉	—	2	1	no	—
82	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×Dic₃₈	—	2	1	no	—
87	C₂×Dic₃₈	—	2	1	no	—
88	C₂×Dic₃₈	—	2	1	no	—
89	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
90	C₂×Dic₃₈	C₂×C₈	1	2	yes	—
91	C₂×Dic₃₈	M₁₆	1	2	yes	—
92	C₂×C₈×C₁₉	—	2	2	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	—
101	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	—
102	C₄²×C₁₉	—	4	1	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	C₄²×C₁₉	#41	1	1	yes	characteristic
107	C₄²×C₁₉	#41	1	1	yes	characteristic
108	C₄⋊Dic₁₉	—	2	1	no	—
109	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
110	Dic₁₉⋊C₄	—	2	4	no	—
111	Dic₁₉⋊C₄	—	2	2	no	—
112	Dic₁₉⋊C₄	—	2	2	no	—
113	Dic₁₉⋊C₄	—	2	4	no	—
114	C₄×Dic₁₉	—	2	4	no	—
115	C₄×Dic₁₉	—	2	2	no	—
116	C₄×Dic₁₉	—	2	2	no	—
117	C₄×Dic₁₉	—	2	1	no	—
118	C₄×Dic₁₉	—	2	1	no	—
119	C₄×Dic₁₉	—	2	1	no	—
120	C₄×Dic₁₉	—	2	1	no	—
121	C₄×Dic₁₉	—	2	4	no	—
122	C₄×Dic₁₉	—	2	2	no	—
123	C₄×Dic₁₉	—	4	1	no	—
124	C₄×Dic₁₉	—	4	2	no	—
125	C₄×Dic₁₉	—	4	2	no	—
126	C₄×Dic₁₉	C₂×C₈	1	2	yes	—
127	C₄×Dic₁₉	M₁₆	1	2	yes	—
128	C₄×Dic₁₉	SD₁₆	1	2	yes	—
129	C₄×Dic₁₉	Q₁₆	1	2	yes	—
130	C₂×C₁₉⋊C₈	—	2	2	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	—	4	1	no	—
136	#8564	—	19	1	no	maximal, Sylow
137	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	4	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	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
160	C₂×Dic₁₉	—	2	2	no	—
161	C₂×Dic₁₉	—	2	2	no	—
162	C₂×Dic₁₉	—	2	1	no	—
163	C₂×Dic₁₉	—	2	2	no	—
164	C₂×Dic₁₉	—	2	1	no	—
165	C₂×Dic₁₉	—	2	1	no	—
166	C₂×Dic₁₉	—	2	1	no	—
167	C₂×Dic₁₉	—	2	2	no	—
168	C₂×Dic₁₉	—	2	1	no	—
169	C₂×Dic₁₉	—	2	1	no	—
170	C₂×Dic₁₉	—	2	1	no	—
171	C₂×Dic₁₉	—	4	1	no	—
172	C₂×Dic₁₉	—	4	1	no	—
173	C₂×Dic₁₉	C₂²⋊C₈	1	2	yes	—
174	C₂×Dic₁₉	C₂²⋊C₈	1	2	yes	—
175	C₂×Dic₁₉	#103	1	2	yes	—
176	C₂×Dic₁₉	#103	1	2	yes	—
177	C₂×Dic₁₉	#104	1	2	yes	—
178	Dic₃₈	—	2	2	no	—
179	Dic₃₈	—	2	2	no	—
180	Dic₃₈	—	2	2	no	—
181	Dic₃₈	C₄⋊C₈	1	4	yes	complemented
182	C₈×C₁₉	—	4	2	no	—
183	C₈×C₁₉	—	8	1	no	—
184	C₁₉⋊C₈	—	4	2	no	—
185	C₁₉⋊C₈	—	8	1	no	—
186	C₄²×Q₈	—	19	1	no	—
187	#1842	—	19	1	no	—
188	C₄×C₄⋊C₈	—	19	1	no	—
189	C₂×Q₈⋊C₈	—	19	1	no	—
190	C₂×Q₈⋊C₈	—	19	1	no	—
191	#1279	—	19	1	no	—
192	#1279	D₁₉	1	1	yes	characteristic
193	C₂²×C₁₉	#380	1	1	yes	characteristic
194	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
195	C₂²×C₁₉	#407	1	1	yes	characteristic
196	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
197	C₂²×C₁₉	#417	1	1	yes	characteristic
198	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
199	C₂²×C₁₉	#421	1	1	yes	characteristic
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
205	C₄×C₁₉	#423	1	1	yes	characteristic
206	C₄×C₁₉	#431	1	1	yes	characteristic
207	C₄×C₁₉	#432	1	1	yes	characteristic
208	C₄×C₁₉	#460	1	1	yes	characteristic
209	C₄×C₁₉	#462	1	1	yes	characteristic
210	C₄×C₁₉	#475	1	1	yes	characteristic
211	C₄×C₁₉	#477	1	1	yes	characteristic
212	Dic₁₉	—	2	4	no	—
213	Dic₁₉	—	2	2	no	—
214	Dic₁₉	—	2	2	no	—
215	Dic₁₉	—	4	2	no	—
216	Dic₁₉	—	4	1	no	—
217	Dic₁₉	Q₈⋊C₈	1	4	yes	complemented
218	C₂×C₄×Q₈	—	19	1	no	—
219	C₂×C₄×Q₈	—	19	1	no	—
220	C₂×C₄×Q₈	—	19	1	no	—
221	C₂×C₄⋊C₈	—	19	1	no	—
222	C₂×C₄⋊C₈	—	38	1	no	—
223	C₂×C₄⋊C₈	—	38	1	no	—
224	C₂×C₄⋊C₈	—	38	1	no	—
225	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
226	C₂×C₄×C₈	—	19	1	no	—
227	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
228	C₄×C₄⋊C₄	—	19	1	no	—
229	C₄×C₄⋊C₄	—	19	1	no	—
230	C₄×C₄⋊C₄	—	38	1	no	—
231	C₄×C₄⋊C₄	—	38	1	no	—
232	C₄×C₄⋊C₄	—	38	1	no	—
233	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
234	C₄³	—	19	1	no	—
235	C₄³	—	38	1	no	—
236	#336	—	38	1	no	—
237	Q₈⋊C₈	—	38	2	no	—
238	Q₈⋊C₈	—	38	2	no	—
239	C₂×C₁₉	C₂×Q₈⋊C₈	1	1	yes	characteristic
240	C₂×C₁₉	#1477	1	1	yes	characteristic
241	C₂×C₁₉	#1487	1	1	yes	characteristic
242	C₂×C₁₉	#1489	1	1	yes	characteristic
243	C₂×C₁₉	#1797	1	1	yes	characteristic
244	C₂×C₁₉	#1803	1	1	yes	characteristic
245	C₂×C₁₉	#1806	1	1	yes	characteristic
246	C₂²×Q₈	—	19	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	38	1	no	—
250	C₂²×C₈	—	38	1	no	—
251	C₄×Q₈	—	19	4	no	—
252	C₄×Q₈	—	19	2	no	—
253	C₄×Q₈	—	19	2	no	—
254	C₄×Q₈	—	38	2	no	—
255	C₄×Q₈	—	38	2	no	—
256	C₄×Q₈	—	38	2	no	—
257	C₄×Q₈	—	38	1	no	—
258	C₄×Q₈	—	38	1	no	—
259	C₂×C₄⋊C₄	—	19	1	no	—
260	C₂×C₄⋊C₄	—	38	1	no	—
261	C₂×C₄⋊C₄	—	38	1	no	—
262	C₂×C₄⋊C₄	—	38	1	no	—
263	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	19	1	no	—
267	C₂×C₄²	—	19	1	no	—
268	C₂×C₄²	—	19	1	no	—
269	C₂×C₄²	—	19	1	no	—
270	C₂×C₄²	—	19	1	no	—
271	C₂×C₄²	—	19	1	no	—
272	C₂×C₄²	—	38	1	no	—
273	C₂×C₄²	—	38	1	no	—
274	C₂×C₄²	—	38	1	no	—
275	C₂×C₄²	—	38	1	no	—
276	C₂×C₄²	—	38	1	no	—
277	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	38	4	no	—
281	C₄⋊C₈	—	38	1	no	—
282	C₄⋊C₈	—	38	1	no	—
283	C₄⋊C₈	—	76	2	no	—
284	C₄⋊C₈	—	76	2	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	—	38	1	no	—
288	C₄×C₈	—	38	1	no	—
289	#95	—	2	1	no	—
290	#95	—	38	1	no	—
291	#95	—	38	1	no	—
292	C₁₉	#8564	1	1	yes	characteristic, complemented, Sylow
293	C₂×Q₈	—	19	2	no	—
294	C₂×Q₈	—	19	2	no	—
295	C₂×Q₈	—	19	2	no	—
296	C₂×Q₈	—	38	1	no	—
297	C₂×Q₈	—	38	1	no	—
298	C₂×Q₈	—	38	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	19	1	no	—
302	C₂²×C₄	—	19	1	no	—
303	C₂²×C₄	—	19	1	no	—
304	C₂²×C₄	—	19	1	no	—
305	C₂²×C₄	—	38	1	no	—
306	C₂²×C₄	—	38	1	no	—
307	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
309	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	38	2	no	—
317	C₂×C₈	—	76	1	no	—
318	C₂×C₈	—	76	1	no	—
319	C₂×C₈	—	76	1	no	—
320	C₂×C₈	—	76	1	no	—
321	C₂×C₈	—	76	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	19	2	no	—
325	C₄⋊C₄	—	38	4	no	—
326	C₄⋊C₄	—	38	4	no	—
327	C₄⋊C₄	—	38	1	no	—
328	C₄⋊C₄	—	38	2	no	—
329	C₄⋊C₄	—	38	2	no	—
330	C₄⋊C₄	C₈×D₁₉	1	2	yes	—
331	C₄⋊C₄	#64515	1	2	yes	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	1	no	—
334	C₄²	—	19	2	no	—
335	C₄²	—	19	2	no	—
336	C₄²	—	19	2	no	—
337	C₄²	—	19	2	no	—
338	C₄²	—	38	2	no	—
339	C₄²	—	38	4	no	—
340	C₄²	—	38	4	no	—
341	C₄²	—	38	2	no	—
342	C₄²	—	38	2	no	—
343	C₄²	—	38	1	no	—
344	C₄²	—	38	1	no	—
345	C₄²	—	38	1	no	—
346	C₄²	—	38	1	no	—
347	C₄²	—	76	1	no	—
348	C₄²	—	76	2	no	—
349	C₄²	—	76	2	no	—
350	C₄²	#64541	1	1	yes	characteristic
351	C₄²	#64541	1	1	yes	characteristic
352	C₄²	D₄×D₁₉	1	1	yes	characteristic
353	C₄²	Q₈×D₁₉	1	1	yes	characteristic
354	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
355	Q₈	—	19	4	no	—
356	Q₈	—	38	2	no	—
357	Q₈	—	38	2	no	—
358	Q₈	—	38	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	19	2	no	—
368	C₂×C₄	—	19	2	no	—
369	C₂×C₄	—	19	2	no	—
370	C₂×C₄	—	19	2	no	—
371	C₂×C₄	—	19	2	no	—
372	C₂×C₄	—	38	1	no	—
373	C₂×C₄	—	38	1	no	—
374	C₂×C₄	—	38	1	no	—
375	C₂×C₄	—	38	2	no	—
376	C₂×C₄	—	38	2	no	—
377	C₂×C₄	—	38	1	no	—
378	C₂×C₄	—	38	2	no	—
379	C₂×C₄	—	38	1	no	—
380	C₂×C₄	—	38	1	no	—
381	C₂×C₄	—	38	2	no	—
382	C₂×C₄	—	38	1	no	—
383	C₂×C₄	—	76	1	no	—
384	C₂×C₄	—	76	1	no	—
385	C₂×C₄	#10597318	1	1	yes	characteristic
386	C₂×C₄	#10597330	1	1	yes	characteristic
387	C₂×C₄	#10597330	1	1	yes	characteristic
388	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
389	C₂×C₄	#10597342	1	1	yes	characteristic
390	C₂×C₄	#10597342	1	1	yes	characteristic
391	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#64515	1	1	yes	characteristic
393	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
394	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
395	C₂×C₄	#10597357	1	1	yes	characteristic
396	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
397	C₂×C₄	#10597361	1	1	yes	characteristic
398	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
399	C₈	—	4	2	no	—
400	C₈	—	8	1	no	—
401	C₈	—	76	2	no	—
402	C₈	—	152	1	no	—
403	C₂²	#11926403	1	1	yes	characteristic
404	C₂²	C₂²⋊C₈×D₁₉	1	1	yes	characteristic
405	C₂²	#11926506	1	1	yes	characteristic
406	C₂²	#103×D₁₉	1	1	yes	characteristic
407	C₂²	#11926542	1	1	yes	characteristic
408	C₂²	#104×D₁₉	1	1	yes	characteristic
409	C₂²	#11926559	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	19	4	no	—
415	C₄	—	38	2	no	—
416	C₄	—	38	4	no	—
417	C₄	—	38	2	no	—
418	C₄	—	76	1	no	—
419	C₄	—	76	2	no	—
420	C₄	C₄⋊C₈×D₁₉	1	1	yes	characteristic
421	C₄	#11926566	1	1	yes	characteristic
422	C₄	#11926595	1	1	yes	characteristic
423	C₄	#11926599	1	1	yes	characteristic
424	C₄	#11926743	1	1	yes	characteristic
425	C₄	#11926753	1	1	yes	characteristic
426	C₄	#11926828	1	1	yes	characteristic
427	C₄	#11926838	1	1	yes	characteristic
428	C₂	D₁₉×Q₈⋊C₈	1	1	yes	characteristic
429	C₂	#14562019	1	1	yes	characteristic
430	C₂	#14562062	1	1	yes	characteristic
431	C₂	#14562071	1	1	yes	characteristic
432	C₂	#14563614	1	1	yes	characteristic
433	C₂	#14563639	1	1	yes	characteristic
434	C₂	#14563654	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1279	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#8564
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
56. #10597333	C₈	semidirect
181. Dic₃₈	C₄⋊C₈	semidirect
217. Dic₁₉	Q₈⋊C₈	semidirect
292. C₁₉	#8564	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597333	2
#14563786	2
C₄×Dic₁₉⋊C₈	2
C₂×#11926276	2
C₂×#11926274	2
#14561476	2
C₁₉×#1279	2
#8564	19